In cities of the second class A, each employe of the office of collector of taxes who became a member of the retirement system in 1962, shall receive full credit toward his pension under this act for each year of service as the employe of a school district collecting such taxes prior thereto, upon his producing proof satisfactory to the pension board of the number of years of such service and upon his making back payments at the same rate as if he had been a city employe, in a lump sum or by installments, as may be determined by the board. If the employe is retired under this act before the back payments have been completed, the annuity shall be reduced by an amount equivalent to the unpaid back payments or deduction increases not anticipated. The contributions required to build up the reserves necessary for the payment of city annuities to such employes, including back payments to match employe back payments, shall be made jointly, one-half each by the city and the school district within the territorial limits of such city. The board of school directors of each such school district and the council of each such city, are hereby authorized and directed to appropriate moneys for the purpose of making such contributions.