Section 59A. If a retired veteran or the widow of a veteran receives a pension from the commonwealth or from a political subdivision thereof under the provisions of section fifty-six, fifty-seven, fifty-eight or fifty-eight B, and if a portion of such pension or widow’s allowance is based on the creditable service of such veteran in a governmental unit other than the unit which pays such pension or allowance, the governmental unit making such payment shall be reimbursed in full by such other governmental unit for such portion of the pension or allowance as shall be computed by the actuary in the public employee retirement administration commission. The treasurer of the governmental unit paying such pension or allowance shall annually, on or before January fifteenth, upon certification of the retiring authority of such governmental unit, notify the treasurer of such other governmental unit of the amount of reimbursement due therefrom for the previous calendar year, and the treasurer of such other governmental unit shall forthwith take such steps as may be necessary to insure prompt payment of such amount. All such payments from the other governmental unit shall be charged to such funds as shall be appropriated for payment of pensions and allowances under section fifty-six, fifty-seven, fifty-eight or fifty-eight B, and when received they shall be credited to and added without further appropriation to such similar appropriation as shall have been made for the payment of similar pensions and allowances in the paying governmental unit. In default of any such payment, the paying governmental unit may maintain an action of contract to recover the same.