If a chief disbursing official or a director of a disbursing center of the Department of the Treasury dies, resigns, or leaves office, the deputy chief disbursing official or the deputy director of the disbursing center designated by the Secretary of the Treasury may continue the accounts and payments in the name of the former disbursing official or director through the last day of the 2d month after the month in which the death, resignation, or separation occurs. The accounts and payments shall be allowed, audited, and settled as provided by law. The Secretary shall honor checks signed in the name of the former disbursing official or director in the same way as if the former disbursing official or director had continued in office.