The department, with the approval of the Attorney General, may compromise in writing, with the person liable, the tax, including interest on the tax, payable on any transfer of property included in the estate of any decedent who it is alleged was a nonresident at the time of his death. A copy of the compromise agreement shall be filed with the register who issued letters, if any, in this Commonwealth; otherwise, it shall be filed with the department. The compromise agreement shall constitute a final determination of the matters covered by it and the payment of the tax, as fixed by the agreement, shall discharge all persons and property from liability with respect to the tax.