(a) "Member" means a contributor to the pension system of any city maintaining a police pension fund based upon the accumulation of deductions from the compensation or the contributions of the members thereof and payments made by such city to pension reserves for such members, and such pension system provides for optional retirement allowances.

(b) "Accumulated deductions" shall mean the sum of all the amounts, deducted from the compensation of a member of such pension system or contributed by him, standing to his credit therein; together with the interest thereon, if any, as provided by the law, charter or administrative code governing such system.

(c) "Pension" shall mean payments for life derived from appropriations for and payments into such pension system by such city.

(d) "Minimum period of service" shall mean a fixed number of years of service specified in a plan or option provided by such police pension system and elected by such member, as a necessary pre-requisite for a pension or retirement allowance upon retirement from service.

(e) "Minimum age" means the age specified in a plan or option provided by such police pension system and elected by such member, as a necessary pre-requisite for a pension or retirement allowance upon retirement from service. 2. Notwithstanding the provisions of any general, special or local law, charter or administrative code, and in lieu of any lesser amount therein prescribed, upon the death of a member, prior to the first payment of a retirement benefit, who has attained the minimum age or completed the minimum period of service, as elected by him for retirement, and whether or not such member shall have filed application for retirement, there shall be paid to his estate, or to such person as he has nominated or shall nominate by written designation duly executed and filed in accordance with the requirements of such respective police pension systems:

(a) His accumulated deductions; and in addition thereto,

(b) The amount of the reserve equal to the present value of the pension he would have received, under the provisions of the law, charter or administrative code governing such police pension system, if he had retired and become entitled to a pension on the day immediately preceding the day of his death. The beneficiary of such deceased member shall have the right to accept such benefits in lump sums or in such periodic payments, on an annuity basis, as such beneficiary shall elect. 3. Nothing contained in the foregoing provisions of this section shall be held or deemed to affect or to lessen any benefits greater than those set forth in the foregoing paragraph two which are or shall be provided for by any such police pension system in respect of a member or members thereof dying in the course of or as the result of the performance of his duties. 4. The provisions of this section shall not apply to members of the New York state and local police and fire retirement system.