Dont know the process for NJ , the NRA might be able to help you with info.
I would keep abreast of the upcoming law changes after Nov 20th as there is an effort being launched in Congress that CCW permit of any states be valid in every state just like the Drivers licenses.
Will be interesting as it is proposed would also allow citizens of states with Constitutional carry to carry in States like NJ as well.

Florida issues CCW permits to non residents as well as full time residents so if the bill passes one could legally get a non resident permit in Florida that would have to be honored in NJ.

Here is a quick resource I found on google Concealed Carry Permit Information By State

BTW I see your a LEO...you cant carry concealed off duty ?