The NJ law was just changed.
Before, if you came from out of state to live in NJ with a handgun you did not have to register it. If you lived in NJ and inherited a gun in NJ I think you had to register it.
Now, with the new NJ laws I think it is necessary to register all handguns if you did not go through the NJ purchase permit process to buy it in the first place.
Long and short of it. If you want a carry permit in NJ make sure you can show you own the gun ( and make sure that you jump through the hoops for ALL the handguns you possess).
PLEASE BE CAREFUL The NJ firearm laws are a trap for the unwary - with the result for violation a felony conviction, loss of liberty and loss of 2A rights everywhere forever.