N.J. Stat. § 3B:14-30
The power of a domiciliary foreign fiduciary under N.J.S. 3B:14-28 or N.J.S. 3B:14-29 shall be exercised only if letters have not been issued or an action therefor is not pending in this State. The issuance of local letters or an action therefor terminates the power of the domiciliary foreign fiduciary to act under N.J.S. 3B:14-29, but a court in this State may allow the domiciliary foreign fiduciary to exercise limited powers to preserve the estate. No person who, before receiving actual notice of local letters or an action therefor, has changed his position in reliance upon the powers of the domiciliary foreign fiduciary, shall be prejudiced by reason of the action for, or issuance of, local letters. The local fiduciary is subject to all duties and obligations which have accrued by virtue of the exercise of the powers by the domiciliary foreign fiduciary and may be substituted for him in any action in this State.
N.J.S. § 3B:14-30