The department shall have authority to enter into reciprocal agreements with corresponding agencies of other states, and to arrange with their local or county boards for the acceptance, transfer and support of persons going from one state to another and becoming public charges and to continue payments of public assistance until eligibility to receive assistance under a similar program has been established in the other state and the first payment from the other state has been received by such recipient. Such reciprocal agreements shall in no way commit the State to support persons who are not, in the opinion of the department, entitled to support under the laws of this State.