Whenever it appears to be to the best interests of the patients concerned, the department shall have the authority to transfer such patients among the various state hospitals pursuant to rules and regulations established by said department. The superintendent of a state hospital shall also have authority to transfer patients eligible for treatment to the veterans administration or other United States government agency where such transfer is satisfactory to such agency. Such agency shall possess the same authority over such patients as the superintendent would have possessed had the patient remained in a state hospital.