Exhibit (a)(5)(iii)​

Dear Shareholder,

The Zweig Fund, Inc. recently announced a tender offer for up to 15% of its issued and outstanding shares of common stock for cash at a price per share equal to 98% of the net asset value per share, as further described in the Fund’s Offer to Purchase dated April 29, 2016 (the “Tender Offer”). Enclosed with this envelope are the materials needed to participate in the Tender Offer.

You are receiving this special letter because our records indicate that you remain in possession of certificated shares of the Fund that were not surrendered in connection with the Fund’s one-for-four reverse stock split that occurred in 2012. The Fund no longer issues certificated shares, and holders are required to surrender such shares to the Fund in exchange for non-certificated shares reflecting the 2012 one-for-four reverse stock split. Shareholders currently holding certificated shares, like yourself, are not able to trade shares represented by the certificates until the certificated shares are surrendered and exchanged for the non-certificated shares. Uncertificated shares are reflected only in the Fund’s record books and are not represented by physical certificates.

If you wish to trade your shares or participate in the Tender Offer, you will first need to surrender and exchange your certificated shares for uncertificated shares that reflect the 2012 one-for-four reverse stock split. Computershare, our exchange agent, has provided to you previously copies of a letter of transmittal to surrender and exchange your certificated shares. An additional copy of that document was most recently mailed to you on April 20, 2016. Regardless of whether you wish to participate in the Tender Offer, if you have not done so already, please complete and return that document as soon as possible to surrender and exchange your certificated shares. Please call Shareholder Services at 1-800-272-2700 if you have any questions regarding the surrender and exchange process.

As described further in the enclosed materials, the Tender Offer will expire on May 26, 2016 (unless extended). Therefore, if you wish to participate in the Tender Offer, you will need to surrender and exchange your certificated shares as soon as possible.

Sincerely,

/s/ Heidi Griswold

Heidi Griswold

Vice President, Mutual Fund Services

This letter is not a recommendation, an offer to purchase, or a solicitation of an offer to sell shares of the Fund. The Tender Offer is being made only by an Issuer Tender Offer Statement, a related Letter of Transmittal and other documents, which have been filed with the Securities and Exchange Commission and are enclosed herein. Shareholders of the Fund should read the Issuer Tender Offer Statement and related exhibits, as they contain important information about the Tender Offer. In addition to being enclosed herein, these and other filed documents are available to investors for free both at the website of the Securities and Exchange Commission and from the Fund. Shareholders may obtain further information regarding the Tender Offer from Georgeson LLC, the Information Agent for the Tender Offer, by calling (866) 413-5901.