Lump-sum benefits authorized by subsections (d)–(f) of this section shall be paid to the person or persons surviving the employee or Member and alive at the date title to the payment arises in the following order of precedence, and the payment bars recovery by any other person: First, to the beneficiary or beneficiaries designated by the employee or Member in a signed and witnessed writing received in the Office before his death. For this purpose, a designation, change, or cancellation of beneficiary in a will or other document not so executed and filed has no force or effect. Second, if there is no designated beneficiary, to the widow or widower of the employee or Member. Third, if none of the above, to the child or children of the employee or Member and descendants of deceased children by representation. Fourth, if none of the above, to the parents of the employee or Member or the survivor of them. Fifth, if none of the above, to the duly appointed executor or administrator of the estate of the employee or Member. Sixth, if none of the above, to such other next of kin of the employee or Member as the Office determines to be entitled under the laws of the domicile of the employee or Member at the date of his death. For the purpose of this subsection, “child” includes a natural child and an adopted child, but does not include a stepchild.