If the amount accumulated in the account of a deceased unmarried fireman from salary deductions for annuity purposes after the effective date, including interest, has not been paid to him or his parent or parents, and in the case of a deceased married fireman to him and his widow, in form of annuity or benefit before the death of the last survivor of such persons, the remaining amount if any, without interest, shall be paid in the following order of precedence: (a) to the administrator or executor of the fireman’s estate; (b) for burial expenses of the fireman; and (c) to his heirs according to the law pertaining to administration of estates; provided, if any of his children less than age 18 survive, such amount as is necessary to pay children’s annuities shall not be refunded, but shall be transferred to the Child’s Annuity Reserve, and used for the payment of annuities to children.