Every authority, the employes of which are members of the fund as hereinabove provided for, shall pay to the board of pensions an amount sufficient to reimburse the board of pensions for the amount of benefits paid employes of such authority, as provided for by the act of which this amendment is a part, after receiving credit for all contributions made to the pension fund by employes of such authority: Provided, however, That where an employe of any authority formerly worked for the city creating the authority, or for the city joining in the creation of the authority, or for the city joining an authority already created, the annual pension requirement or other benefits shall be prorated on the basis that the number of years such employe worked for the authority bears to total years of service in city and authority employment, and the authority shall reimburse the board of pensions for that proportionate part of the pension or other benefits paid which the authority service bears to the total, and the balance of annual pension requirements or other benefits shall be paid by such cities.

Every authority employe shall have the option of joining or refusing to join the pension fund on or before March 1, 1960, or within twelve months of the date when the privilege of joining occurs, whichever is later. Any authority employe shall receive full credit toward his pension under the act for each year of service as the employe of the authority, upon his producing proof satisfactory to the pension board of the number of years of his service as an employe of the authority, 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.