Will there be a problem if my executrix (and sole heir) lives in Florida and I live in NJ?

I do not believe this will be a problem at all.  I deal with many estates where the Executrix lives in another state, or even another country.  Things can be done by mail or email, over the phone, or with a few trips to New Jersey.  Its helpful if the Executrix has a lawyer to assist her coordinating paperwork, but its not difficult.