(a) All credit for military service, out-of-state service, developmental leave, work experience in a career or technological field, and service transferred to the retirement system under Chapter 805 shall be computed on a September 1 through August 31 school year. Payments for service described by this section must be completed:
(1) not later than two calendar months after the later of the member's retirement date or the last day of the month in which the member submits a retirement application; and
(2) before the later of the due date for the member's first monthly annuity payment or the date on which the retirement system issues the first monthly annuity payment to the member.
(b) The retirement system by rule may establish an irrevocable employer pick-up of member contributions as described by Section 414(h)(2) of the Internal Revenue Code of 1986 (26 U.S.C. Section 414(h)(2)) for the purchase of any service credit authorized by law.