Fair Access to Co-ops for Veterans Act - Revises the Department of Veterans Affairs (VA) program that guarantees veterans' loans for the purchase of residential cooperative housing to remove a provision that limits to five years after a loan is guaranteed the use of loan proceeds to purchase stock or membership in a cooperative housing corporation. Directs the Secretary of Veterans Affairs to ensure that a loan used for such purchase in a corporation that has been reviewed and approved by a lender approved by the Federal National Mortgage Association (Fannie Mae) is not denied. Authorizes the Secretary to advertise the availability of such loan guarantees.