N.H. Rev. Stat. Ann. § 464-A:16

At any time upon petition signed by the protected person, the court shall direct the termination of the conservatorship and the transfer of all property held thereunder to the protected person. Likewise, if at any time subsequent to the appointment of a conservator it shall appear that the protected person has died and an executor or administrator has been appointed for his or her estate, the court shall direct the termination of the conservatorship and the transfer of all property of the deceased person held thereunder to such executor or administrator.