In any case in which an election is made as provided in § 1702 of this title and not rejected, the Secretary of Finance 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. Such agreement shall not be effective unless approved by the State Tax Appeal Board. If an agreement cannot be reached and the arbitration proceeding specified in § 1704 of this title is commenced and thereafter an agreement is arrived at, a written agreement may be entered into at any time before the arbitration proceeding is concluded. Upon the filing of such agreement or duplicate thereof 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 of the amount of tax agreed upon shall be made, and such assessment shall finally and conclusively fix and determine the amount of death tax due this State.