Where the Attorney General claims that transferred property has a tax situs in this State and the taxing authorities of another state or states claim the same transferred property is subject to a transfer tax in their state or states, the Attorney General may enter into a written agreement with those taxing authorities in the other state or states and with the person required to file the Illinois transfer tax return or pay the Illinois transfer tax that a certain sum shall be accepted in full payment of the tax imposed by this Act, provided that the agreement also fixes the amount to be paid in full payment to such other state or states. Full power and authority is hereby conferred upon the person required to file the Illinois transfer tax return or pay the Illinois tax to enter into the agreement provided for in this Section.