Upon receipt of proper proof of death of a member who does not qualify for the death benefit of six hundred dollars under RCW
41.32.522, or a former member who was retired for age, service, or disability, a death benefit of four hundred dollars shall be paid to the member's estate or to the persons, trust, or organization as he or she shall have nominated by written designation duly executed and filed with the department or to the persons as may otherwise qualify as the beneficiary pursuant to RCW
41.32.520: PROVIDED, That the member or the retired former member had established not less than ten years of credit with the retirement system for full time Washington membership service.