N.J. Stat. § 38:18A-4
Any veteran or surviving spouse receiving payments pursuant to the provisions of P.L. 1947, c. 263 (C. 38:18A-1 et seq.) and who is required to, and who does, move without the State for reasons of health or employment, and any veteran who heretofore was receiving payments pursuant to the provisions of P.L. 1947, c. 263 (C. 38:18A-1 et seq.) and who was required to, and who did, move without the State for reasons of health or employment, shall notwithstanding such nonresidence be entitled to continue to receive such payments. In the event such veteran or surviving spouse becomes entitled to payments from the state to which he moves pursuant to an act of such state substantially similar to this act and P.L. 1947, c. 263 (C. 38:18A-1 et seq.), such payments shall immediately cease, unless such veteran or surviving spouse shall elect to receive such payments to the exclusion of the payments of the state to which he moves.
N.J.S. § 38:18A-4