Exhibit A

THE ENDOWMENT INSTITUTIONAL TEI FUND W, L.P.

c/o Endowment Advisers, L.P.

4265 San Felipe, 8^th Floor

Houston, Texas 77027

To the Investor of The Endowment Institutional TEI Fund W, L.P.:

As previously disclosed in Item 3 of the Offer to Purchase dated July 24, 2012, if the offer to repurchase limited partnership interests (“Interests”) of The Endowment Institutional TEI Fund W, L.P. (the “Fund”) is oversubscribed at the expiration date of 12:00 midnight, Central Time, on August 21, 2012 and not withdrawn pursuant to the terms of the Offer to Purchase and related Letter of Transmittal (the “Offer”), the Fund may, in its sole discretion take one or more actions, including extending the Offer and increasing the amount of Interests that the Fund is offering to purchase to an amount it believes sufficient to accommodate the excess Interests tendered, as well as any Interests tendered during the extended Offer.

Because the amount of Interests tendered exceeded the amount of Interests in the original Offer, the Fund has decided to extend the Offer until 12:00 midnight, Central Time, on September 14, 2012, and increase the amount of Interests the Fund is offering to purchase to an aggregate of $25,000,000. All of the other terms of the original Offer remain unchanged.