A member retired after January 1, 1965 shall have his or her credited service include service rendered by him or her to the university of Michigan, Michigan state university, Wayne state university, Oakland university, Grand Valley state university and Saginaw valley state university to the same extent that service would have been credited had it been rendered in a position covered under this act, if the member pays into the employees’ savings fund the contributions, together with regular interest, he or she would have paid had his or her service been rendered in a position covered under this act and if the member relinquishes for himself or herself and his or her beneficiary all rights in and to a retirement allowance for service rendered to the university of Michigan, Michigan state university, Wayne state university, Oakland university, Grand Valley state university and Saginaw valley state university.