If any military or overseas voter returns to the county of his or her residence, or for a military or overseas voter qualified pursuant to paragraph (2) of subdivision (b) of Section 321, to the county in which the applicant’s parent or legal guardian resided when the parent or legal guardian last lived within the territorial limits of the United States or the District of Columbia, after the final day for making application for a vote by mail ballot, he or she may appear before the elections official and make application for registration, vote by mail ballot, or both. The elections official shall register the voter, if he or she is not registered, and deliver to him or her a vote by mail ballot which may be voted in the elections
official’s office or voted outside the elections official’s office on or before the close of the polls on the day of election and returned as are other vote by mail ballots.