The State Department of Developmental Services may transfer any patient of a state hospital for the developmentally disabled to another state hospital for the developmentally disabled, at any time and from time to time, upon the application of the parent, guardian, conservator, or other person charged with the support of such patient, if the expenses of the transfer are paid by the applicant. The liability of any estate, person, or county for the care, support and maintenance of such patient in the institution to which he is transferred shall be the same as if he had originally been committed to such institution.