Any member retiring pursuant to the provisions of this chapter or any member retiring pursuant to provisions of chapter 169 who is a member of the public school retirement system and who is employed by a department other than an institution of higher learning, after working continuously until reaching retirement age, shall be credited with all his or her unused sick leave as reported by the last department that employed the member prior to retirement through the financial and human resources system maintained by the office of administration, or if a state agency’s employees are not paid salaries or wages through such system, as reported directly by the last department that employed the member prior to retirement. When calculating years of service, each member shall be entitled to one-twelfth of a year of creditable service for each one hundred sixty-eight hours of unused accumulated sick leave earned by the member. The employing agency shall not certify unused sick leave unless such unused sick leave could have been used by the member for sickness or injury. The rate of accrual of sick leave for purposes of computing years of service pursuant to this section shall be no greater than ten hours per month. Nothing under this section shall allow a member to vest in the retirement system by using such credited sick leave to reach the time of vesting.