If you have already contacted the Social Security Administration (SSA) and have proof of their agreement to the changes/corrections you can file your return with the correct information. When you get the corrected document place it with your tax records.
Be diligent to follow up until you have something in writing if you don't have anything now. An explanation is not necessary to send with your return at this time. However, if you choose to send any documentation you can print your Form 8879 (assuming you e-file) and mail it with your document to the following address. Otherwise you can attach them to the front of the Form 1040 if filed by mail.
Internal Revenue ServiceAttn: Shipping and Receiving, 0254Receipt and Control BranchAustin, TX 73344-0254