N.H. Rev. Stat. Ann. § 552:13

A duly authenticated copy of a will made out of this state, which has been proved and allowed by a court of probate or by a court of similar powers in one of the United States, or in a foreign country, and a duly authenticated copy of the probate of such will, upon the written application of a party in interest, and upon such citation and notice as the court shall order, may, by a decree of the court of probate, be filed and recorded in the probate office; and thereupon the will shall have the same effect as if executed with the formalities required by the laws of this state and duly proved and allowed.