The Governor of the state is empowered and directed to receive from the United States all money that may be due or may become due to the state, and it shall be his or her duty to deposit the same without delay in the treasury of the state, taking the State Treasurer’s receipts therefor. All money received from the United States, for the particular benefit of any institution, department, or activity under the jurisdiction of the Department of Health and Human Services or the Department of Correctional Services, shall be paid to the particular institution, department, or activity for the benefit of which it was received, as directed by the proper department, and by such institution, department, or activity deposited with the State Treasurer not later than the first day of the month following that in which received.