In any case in which an election is made as provided in N.H. Rev. Stat. § 90:2 and not rejected, the department of revenue administration 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 said 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 N.H. Rev. Stat. § 90:4 is commenced, and thereafter an agreement is arrived at, a written agreement may be entered into at any time before such proceeding is concluded, notwithstanding the commencement of such proceeding. Upon the filing of such agreement or duplicate thereof with the department of revenue administration, an assessment shall be made as therein provided and such 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 such agreement to the states involved is less than the maximum credit allowable to the estate against the United States estate tax imposed with respect thereto, the executor forthwith shall also pay to the department of revenue administration the same percentage of the difference between such aggregate amount and the amount of such credit, as the amount payable to this state under the agreement bears to such aggregate amount.