To facilitate the settlement of the accounts of the deceased employees, money due an employee at the time of the employee's death shall be paid to the person or persons surviving at the date of death, in the following order of precedence, and the payment bars recovery by another person of amounts so paid:

(a) First, to the beneficiary or beneficiaries designated by the employee in a writing received in the employing agency prior to the employee's death;

(b) Second, if there is no designated beneficiary, to the surviving spouse of the employee;

(c) Third, if none of the above, to the child or children of the employee and descendants of deceased children by representation;

(d) Fourth, if none of the above, to the parents of the deceased employee or the survivor of them;

(e) Fifth, if none of the above, to the duly appointed legal representative of the estate of the deceased employee; and

(f) Sixth, if none of the above, to the person or persons entitled under the laws of the domicile of the employee at the time of his or her death.