(1) A member may transfer or purchase service credit earned when the member was an employee of a city with a population over 750,000 if all of the following apply:

  (a) The member became a member on September 1, 1981.

  (b) The member was employed by a city with a population over 750,000 on August 31, 1981.

  (c) The pension system of the city with a population over 750,000, the city with a population over 750,000, or the member agrees to contribute the actuarial cost of the service credit transferred or purchased to the retirement system.

  (2) Upon payment of the actuarial cost of the service credit purchased, the retirement system shall credit the member with the service.