Exhibit (a)(1)(H)

Offer to Amend Eligible Options

November 2008

What is Comverse Offering?

The Reason and Purpose of the Offer

Why is the Offer made to You?

Section 409A and its Adverse Tax Consequences

How the Change to the Exercise Price Works?

If Offer Expiration Date FMV Is Less Than Original Exercise Price

If Offer Expiration Date FMV Is Higher Than Original Exercise Price

Am I Required to Participate in the Offer?

Procedures for Participating in the Offer

Offer Timeline

Election Form

Notice of Receipt of Election Form and Final Election Confirmation Statement

Changing an Election

Tender Agent for the Offer

Information Agent for the Offer

Terms and Conditions of the Offer

Additional Considerations – Incentive Stock Options (“ISOs”)

Disclaimer

What is Comverse Offering?

Comverse is offering to change the exercise price of
your outstanding and unexercised eligible discounted
options to a new exercise price equal to the lesser of:

1.

The fair market value⁽¹⁾ of Comverse common stock on the
options’ correct measurement date⁽²⁾; or

2.

The fair market value on the expiration date of the Offer

⁽¹⁾   In determining the fair market value of our common stock on a given date, we use the closing
price of our common stock on the Nasdaq Stock Market or “Pink Sheets”, as applicable.  In this
presentation we will sometime refer to fair market value as “FMV”.

⁽²⁾   Measurement date means the actual revised date of grant of your options as determined for
financial reporting purposes by the Special Committee of the Board of Directors of Comverse as
part of its investigation of Comverse’s historical stock option grant practices.

What is Comverse Offering? (cont’d)

If the new exercise price is higher than the original exercise price,
Comverse will also make a cash payment (less applicable tax
withholding) to you, determined by multiplying:

The number of shares subject to the “eligible portion” of
eligible options being amended, and

The amount by which the new exercise price exceeds the
original exercise price

All other terms of the options will remain unchanged

The Reason and Purpose of the Offer

IRS permits companies to “cure” unexercised discounted options
(such that they comply with Section 409A) if their exercise prices
are amended prior to December 31, 2008

The purpose of the offer is to mitigate the personal tax
consequences under Section 409A of the Internal Revenue Code
by “curing” the options

It is your choice to accept or reject the Offer being made by
Comverse

Why is the Offer made to You?

You hold options which:

Were granted with an exercise price per share that is less than the
fair market value of the underlying shares on the date of grant; and

Were unvested as of December 31, 2004

Our information indicates that you are subject to United States
federal income tax

You may be subject to adverse tax consequences

Section 409A and its Adverse Tax Consequences

The Special Committee of the Board of Directors has determined
that certain options were granted, for accounting purposes, with an
exercise price that is less than the fair market value per share of the
underlying Comverse common stock subject to such options on the
applicable “measurement date”

As a result;

Section 409A provides that certain “discounted options” that are
unvested as of December 31, 2004 are considered deferred
compensation arrangements and are subject to the adverse tax
consequences described on the next slide

These options may be deemed to be “discounted” for tax
purposes

Section 409A and its Adverse
Tax Consequences (cont’d)

Adverse Tax Consequences - if the discounted options are not
amended, you may be subject to the following adverse tax
consequences:

Immediate recognition of income on the option spread (i.e., the
difference between the fair market value of the aggregate option
shares and the aggregate exercise price for such shares) even if
you do not exercise the options and do not realize any gain

An additional 20% federal tax under Section 409A, plus certain other
state and federal tax penalties (including state taxes that may
duplicate the additional tax imposed under Section 409A) on the
spread  

Application of interest if the income should have been recognized in
an earlier year than first reported

Administrative burden - If the discounted options are not
amended, you will be required to amend your tax returns for tax
years beginning on the first year in which the income should have
been recognized

If

FMV on the Offer expiration date is $8,

The original exercise price is $16.70,
and

The FMV on the correct measurement
date is $16.79,

How the Change to the Exercise Price Works?
If Offer Expiration Date FMV is less than Original Exercise Price

The new exercise price will be lower than the original exercise price as
follows:

If the FMV on the Offer expiration date is less than the original exercise
price, then

The FMV on the Offer expiration date would become the new exercise price,

No cash payment would be made to participating holders, and

The other terms of the options would remain unchanged

For example

Then

The new exercise price would be
decreased to $8,  

No cash payment would be made to you,
and

You would have the same number of
options but at the new lower exercise
price

How the Change to the Exercise Price Works? (cont’d)
If Offer Expiration Date FMV is Higher than Original Exercise Price

The new exercise price will be higher than the original exercise
price and you will receive a cash payment equal to the increase
(less applicable withholding tax) as follows:

If the FMV on the Offer expiration date is greater than the
original exercise price but less than the FMV on the correct
measurement date, then:

The new exercise price would increase to the FMV on the Offer
expiration date, and

Cash payment will be paid

For example

If

The original exercise price is $16.70,

FMV on the Offer expiration date is
$16.75, and

The FMV on the correct measurement
date is $16.79

Then

The new exercise price would be
increased to $16.75,

A cash payment of $0.05 per share
would be made to you, and

The other terms of your options would
remain unchanged

How the Change to the Exercise Price Works? (cont’d)
If Offer Expiration Date FMV is Higher than Original Exercise Price

If the FMV on the Offer expiration date is greater than the
original exercise price and the FMV on the correct
measurement date, then:

The new exercise price would increase to the FMV on the correct
measurement date, and

Cash payment will be paid

For example

If

The original exercise price is $16.70,

The FMV on the correct measurement
date is $16.79, and

FMV on the Offer expiration date is
$16.90,

Then

The new exercise price would be
increased to $16.79,

A cash payment of $0.09 per share
would be made to you, and

The other terms of your options would
remain unchanged

How the Change to the Exercise Price Works? (cont’d)
If Offer Expiration Date FMV is Higher than Original Exercise Price

Cash Payments

Payment of a special cash payment to you in January 2009 will
be determined by multiplying:  

The number of shares subject to the “eligible portion” of the
eligible option, and

The amount by which the increased new exercise price exceeds
the original exercise price

Applicable withholding taxes will be deducted from such
payment

How the Change to the Exercise Price Works? (cont’d)
If Offer Expiration Date FMV is Higher than Original Exercise Price

If cash payments are due under the Offer, you will be entitled to
receive such cash payments regardless of whether you remain
employed with Comverse or any of its subsidiaries on the actual
payment date and regardless of whether your amended option to
which such payment relates vested or ever vests

If any cash payment is required, Comverse will extend the
expiration time of the Offer to 5:30 p.m., U.S. Eastern Time, on
December 31, 2008 and pay you such cash payments promptly
after the expiration of the Offer as required under applicable
securities laws.  However, in compliance with Section 409A, no
cash payment can be made to you before January 1, 2009

Am I Required to Participate in the Offer?

No.  You are not required to participate in the Offer

Your decision to accept or reject the Offer will have no effect on
your eligibility to receive additional option grants or other equity
awards in the future from Comverse

Adverse personal tax consequences under Section 409A (and
similar state tax laws of similar effect) may apply to any eligible
option if it is not amended pursuant to the Offer, and you will be
solely responsible for any taxes, penalties, or interest payable
under Section 409A

Procedures forParticipating in the Offer

(*)    If the FMV on the expiration date of the Offer is higher than the original exercise price of your options:

We intend to extend the expiration time of the Offer to 5:30 p.m., U.S. Eastern Time, on December 31,
2008, and

Cash payments (less applicable withholding tax) will be made to you in January 2009 promptly following
the expiration time of the Offer

Offer Timeline

                            Offer Launch

Election Form
Submitted to
Tender Offer
Agent

Notice of Receipt
of Election Form

Offer Expiration
Time (*)

Final Election
Confirmation
Statement (*)

Three Business
Days

Three Business
Days

Procedures for Participating in the Offer (cont’d)

Election Form

You will be receiving with the Offer documents a personalized Election Form

To participate in the Offer, you are required to:

Complete and sign the Election Form; and

Submit a copy of your completed Election Form to the Tender Agent by hand delivery,
mail, overnight delivery, facsimile or email

In the Election Form, you need to mark your election by checking the appropriate
box for each of your eligible options if you elect to amend

Even if you elect not to participate in the Offer, we urge you to complete and
submit an Election Form

Your Election Form must be received by 5:30 p.m., U.S. Eastern Time, on
December 18, 2008 (or a later termination time if we extend the Offer)  

Please keep a copy of your Election Form(s) for your records  

If you submit your Election Form by email to the Tender Agent, please use the
“delivery receipt” option in Outlook and print a copy of the delivery receipt that is
sent to you

Procedures for Participating in the Offer (cont’d)

Notice of Receipt of Election Form and Final Election
Confirmation Statement

Within three business days after your Election Form is
received, you will receive a Notice of Receipt of Election
Form from the Tender Agent

Within three (3) business days after the expiration time of the
Offer, you will receive a Final Election Confirmation
Statement that confirms the last election that you made

If you receive the Notice of Receipt of Election Form(s) and
Final Election Confirmation Statement by email, please print
and keep a copy of such documents  

Procedures for Participating in the Offer (cont’d)

If you do not receive a Notice of Receipt of Election Form(s) or
Final Election Confirmation Statement confirming your elections in
the time frames described, please:

1.

Contact the Tender Agent, and

2.

Send your printed copies of your last Election Form, email delivery
receipt (if you submitted your election Form by email) and any
Notice of Receipt of Election Form or Final Election Confirmation
Statement that you did receive to the Tender Agent to evidence
proper and timely submission of your Election Form

If you have any questions about submitting your Election Form, or if
you do not receive your Notice of Receipt of Election Form(s) or
your Final Election Confirmation Statement, please contact the
Information Agent

Procedures for Participating in the Offer (cont’d)

Changing an Election

To change your election, you must submit a new Election Form
to the Tender Agent by hand delivery, mail, overnight delivery,
facsimile or email

You may change or withdraw your election at any time before
5:30 p.m., U.S. Eastern Time, on December 18, 2008 (or a
later expiration date if we extend the Offer)

The Tender Agent for the Offer is:

D.F. King & Co., Inc.

By E-mail:

comverse@dfking.com

By Facsimile:

(212) 809-8838

To Confirm Receipt Please Call:

(212) 493-6996

By Hand, Mail or Overnight Delivery:

D.F. King & Co., Inc.

Attn: Mark Fahey

48 Wall Street, 22^nd Floor

New York, New York  10005

The Information Agent for the Offer is:

D.F. King & Co., Inc.

48 Wall Street

22nd Floor

New York, NY  10005

Inside the United States, Please Call:(800) 290-6427

Outside the United States, Please Call Collect: (212) 269-5550

Terms and Conditions of the Offer

Options granted on the following dates that were unvested (in
whole or in part) as of December 31, 2004 and which remain
outstanding and unexercised (in whole or in part) are “eligible
options”

  Comverse Technology, Inc. 1996 Stock Option Plan

  Comverse Technology, Inc. 1997 Stock Incentive Compensation Plan

  Comverse Technology, Inc. 1999 Stock Incentive Compensation Plan

  Comverse Technology, Inc. 2000 Stock Incentive Compensation Plan

  Boston Technology, Inc. 1994 Stock Incentive Plan

  Boston Technology, Inc. Amended and Restated 1996 Stock Incentive Plan

$16.70

12/19/2003

Boston Technology, Inc. Amended and Restated 1996 Stock Incentive
Plan

$14.68

8/15/2003

Comverse Technology, Inc. 2001 Stock Incentive Compensation Plan

$16.05

10/22/2001

Comverse Technology, Inc. 1999 Stock Incentive Compensation Plan

$52.97

4/9/2001

Plans Under Which Eligible Options Were Issued

Original Option
Exercise Price

per share ($)

Original
Date
of Grant

Terms and Conditions of the Offer (cont’d)

Each eligible option that is amended pursuant to the Offer will
generally have the same material terms and conditions as it did
prior to the amendment, including the same exercise and vesting
schedule and expiration date, except that the “eligible portion” (i.e.,
the portion which was unvested as of December 31, 2004 and
which remains outstanding and unexercised) of an amended option
will have a new exercise price and new deemed date of grant.  The
amendment of the “eligible portion” of an eligible option pursuant to
the Offer will not affect the terms and conditions of the ineligible
portion of such eligible option

Additional Considerations-
Incentive Stock Options (“ISOs”)

Certain of the Eligible Options were originally granted with the
intention that such awards would qualify as ISOs as defined for tax
purposes

As a result of uncertainty as to whether the IRS will respect our
original determination of the grant date for Eligible Options, there
can be no assurance that the Eligible Options granted as ISOs will
be respected by the IRS or that such Eligible Options are not
subject to Section 409A

Therefore, Comverse will be treating all Eligible Options as non-
qualified stock options from and after the date on which this Offer
commences, including Eligible Options that were intended to qualify
as ISOs regardless of whether an Eligible Optionee participates in
the Offer

Disclaimer

We note that the Offer is subject to the risks set forth in the section of the
Offer to Amend Eligible Options entitled “Risk Factors Relating to the Offer”

Comverse believes that as a result of the amendments described herein,
the “eligible portion(s)” of your eligible options should no longer be subject
to the adverse personal tax treatment of Section 409A (and state tax laws
of similar effect)

However, you should note that the application of Section 409A (and any
state tax laws of similar effect) to the “eligible portion(s)” of the eligible
options, as amended pursuant to Offer, is not entirely free from doubt and
Comverse makes no representations as to the effect of this Offer on the
application of Section 409A and similar state taxes

WE URGE YOU TO CONSULT WITH YOUR PERSONAL FINANCIAL,
TAX AND LEGAL ADVISORS TO DETERMINE THE CONSEQUENCES
OF ELECTING OR DECLINING TO PARTICIPATE IN THE OFFER