N.J. Stat. Ann. § 16:1-21

The new corporation shall be entitled to, and invested with, all the real and personal property, assets, rights, privileges, powers and franchises belonging to each of the societies so consolidated or united, but subject to all the debts and liabilities of each, and to the terms of the agreement under which such consolidation or union was made. It shall also possess and exercise all the powers, rights, privileges and franchises which any religious society of like denomination may possess and exercise when incorporated under the existing laws of this state.