(3)
the amendment changes the party or the naming of the party against whom a claim is asserted if the foregoing provision (2) is satisfied and, within the period provided by Rule
4
(m) for service of the summons and complaint, the party to be brought in by amendment (A) has received such notice of the institution of the action that the party will not be prejudiced in maintaining a defense on the merits, and (B) knew or should have known that, but for a mistake concerning the identity of the proper party, the action would have been brought against the party.
The delivery or mailing of process to the United States Attorney, or United States Attorney’s designee, or the Attorney General of the United States, or an agency or officer who would have been a proper defendant if named, satisfies the requirement of subparagraphs (A) and (B) of this paragraph (3) with respect to the United States or any agency or officer thereof to be brought into the action as a defendant.