(a) A lump-sum death benefit in the amount of $5,000 is payable if the board of trustees receives proof satisfactory to it of the death, on or after September 1, 1975, of a person retired under a retirement system administered by the board. The board by rule shall adopt procedures to provide for the payment of this benefit not later than the seventh day after the date the board receives the required proof of death.
(b) The benefit provided by this section is payable to a person designated by the retiree in a signed and witnessed document filed with the retirement system before the retiree’s death. A designation, change, or revocation of a beneficiary in a will or other document not filed with the retirement system is not effective. If a retiree does not designate a beneficiary or if the beneficiary designation cannot be made effective, the benefit is payable to the retiree’s estate.

(c) A beneficiary designation that names a former spouse as beneficiary is invalid for purposes of this section unless the designation is made after the date of the divorce.