We may correct the record of your earnings to remove, reduce, or enter earnings for work in the employ of the United States only if—

(a) Correction is permitted under § 404.821 or § 404.822; and

(b) Any necessary determinations concerning the amount of remuneration paid for your work and the periods for which such remuneration was paid have been made as shown by—

(1) A tax return filed under section 3122 of the Internal Revenue Code (26 U.S.C. 3122); or

(2) A certification by the head of the Federal agency or instrumentality of which you have been an employee or his or her agent. A Federal instrumentality for these purposes includes a nonappropriated fund activity of the armed forces or Coast Guard.