When a register claims that a decedent was domiciled in this State at the time of death and the taxing authority of another state makes a similar claim on behalf of that state, then, with the approval of the Attorney General of this State, the Comptroller may make a written agreement of compromise with the other taxing authority and the personal representative that a certain sum shall be accepted in full satisfaction of all death taxes imposed by this State, including any interest or penalties to the date of filing the agreement. The agreement also shall determine the amount to be accepted by the other state in full satisfaction of death taxes. The personal representative may make the agreement.