N.J. Stat. Ann. § 2A:42-4

When premises shall be underlet by any tenant, the undertenant shall be liable to the lessor or landlord for the rent which shall accrue from and after notice in writing served for that purpose upon the undertenant, or which shall be unpaid by the undertenant at the time of such notice, and the lessor or landlord shall have all the remedy for the recovery of the same by distress; but the rent to be paid by such undertenant shall in no case exceed the amount agreed to be paid by the first tenant. If only a part of the premises shall be underlet, payment shall be required only for the part underlet, at a rate proportioned to the rent agreed to be paid by the first tenant or lessee.