It would allow carry in NJ with a non-resident PA permit..
(a) Notwithstanding any provision of the law of any State or political subdivision thereof, related to the carrying or transportation of firearms, a person who is not prohibited by Federal law from possessing, transporting, shipping, or receiving a firearm, and who is carrying a government-issued photographic identification document and a valid license or permit which is issued pursuant to the law of a State and which permits the person to carry a concealed firearm, may carry a concealed handgun (other than a machinegun or destructive device) that has been shipped or transported in interstate or foreign commerce, in any State, other than the State of residence of the person, that—
(1) has a statute that allows residents of the State to obtain licenses or permits to carry concealed firearms;
Let me string those together..
"a person...who is carrying a government-issued photographic identification document and a valid license or permit which is issued pursuant to the law of a State...may carry a concealed handgun".Notice it says "a State", not the person's state of residence.