As far as I know there is no reciprocity between NJ and other states with respect to licenses and business permits. Technically speaking, I'm not supposed to even "help" my neighbor do any electrical work as a licensed electrician. Anyone without a NJ license and a business permit cannot legally contract electrical work with the public. Having said that, if a HO wants to pull a permit and assume all responsibility he is permitted to do so. You can write a check to a relative but not "specifically" for electrical work.
BTW, Mike Holt had once published a list of states and their licensing policies. If I find it I'll post it here.