In any case in which an election is made as provided in § 44-23-28 and not rejected, the tax administrator may enter into a written agreement with the other taxing officials involved and with the executors, to accept a certain sum in full payment of any death tax, together with interest and penalties, that may be due this state; provided, that the agreement also fixes the amount to be paid the other state or states. If an agreement cannot be reached and the arbitration proceeding specified in § 44-23-30 is commenced, and thereafter an agreement is arrived at, a written agreement may be entered into at any time before the proceeding is concluded notwithstanding the commencement of the proceeding. Upon the filing of the agreement or duplicate of it with the authority which would have jurisdiction to assess the death tax of this state if the decedent died domiciled in this state, an assessment shall be made as provided in the agreement. The assessment, except as hereinafter provided, shall finally and conclusively fix and determine the amount of death tax due this state. In the event that the aggregate amount payable under the agreement to the states involved is less than the maximum credit allowable to the estate against the United States estate tax imposed with respect to the tax, the executor shall also immediately pay to the taxing administrator that percentage of the difference between the aggregate amount and the amount of the credit, which the amount payable to the taxing administrator under the agreement bears to the aggregate amount.