The board of elections shall keep a record of the name and address of each person to whom the board mails or delivers uniformed services or overseas absent voter’s ballots, the kinds of ballots so mailed or delivered, and the name and address of the person who made the application for such ballots. After the board has mailed or delivered such ballots the board shall not mail or deliver additional ballots of the same kind to such person pursuant to a subsequent request unless such subsequent request contains the statement that an earlier request had been sent to the board prior to the thirtieth day before the election and that the uniformed services or overseas absent voter’s ballots so requested had not been received by such person prior to the fifteenth day before the election, and provided that the board has not received an identification envelope purporting to contain marked uniformed services or overseas absent voter’s ballots from such person.