The appropriate official of the United States Department of Veterans Affairs or other agency of the United States shall have authority to transfer any person committed to the United States Department of Veterans Affairs or other appropriate agency of the United States or to a hospital maintained by either to any other hospital operated by the United States Department of Veterans Affairs or any other agency of the United States, to any licensed private institution, or, subject to the prior approval of the Department of Health and Human Services, to any Nebraska state hospital for the mentally ill. The Department of Health and Human Services, upon written consent of the legal guardian of the patient or the written approval of the county board of mental health which committed such patient if no such guardian has been appointed, shall have the authority, subject to eligibility and the prior approval of the appropriate official of the United States Department of Veterans Affairs or other appropriate agency of the United States Government, to transfer for care or treatment any patient committed to a Nebraska state hospital for the care of the mentally ill to the United States Department of Veterans Affairs or other appropriate agency of the United States Government. Upon any such transfer and notice thereof by mail to the committing court or the judge thereof or the committing board, the original commitment of such person shall be deemed to constitute commitment to the United States Department of Veterans Affairs or other agency of the United States or to the state hospital or licensed institution to which such person may, from time to time, be so transferred.