N.J. Stat. Ann. § 54:37-4

Within thirty days after the original, not ancillary, qualification in a probate court of this state of an executor of the will of, or administrator of the estate of, a nonresident decedent, notice thereof, by mail, shall be given by the clerk of such probate court to the official or body of the domiciliary state charged with the administration of the death tax law thereof with respect to such estate. Such notice shall state the full name of the decedent, date of decedent's death, name of the county and state wherein he resided at the date of death, and the name and address of each person to whom letters have been issued.