No specific statute covers transferring a firearm to an out-of-state FFL - so the only applicable statutes are the ones regarding possession of the firearm, and it's transportation to the facility that will then ship it to the FFL in question.

If we're talking a long gun, then as long as the current owner has an FID card, there's no issue with boxing it up, and transporting it (unloaded of course) to any shipping facility.  UPS/FedEx or Post Office are all valid means of shipping to an FFL.  The only cite I can give you here is 2C:39-5c, which says it's unlawful to possess a rifle or shotgun unless one first obtains an NJ FID card.

If we're talking a handgun, then there is actually no legal way to transport it to FedEx or UPS (as you can't send a handgun via USPS without possessing an FFL).  And, there's no legal way to transport it to a local FFL "for the purposes of transferring it to another FFL".  To comply with the provisions of 2C:39-6f, one would either need to transport it to an FFL for the purposes of repair - and THEN while there, decide to transfer it to another FFL.  Or, if said FFL also has a range on-prem, transport it there for the purposes of target shooting, and THEN after shooting it, decide to send it to another FFL.

You could also send it to the receiving FFL directly, and issue a FedEx or UPS call tag to have it picked up from your residence, thereby avoiding the transportation problem altogether.

No problem sending to an out of state FFL, but it would be wise to call first and obtain a copy or at least his FFL number and check to insure it it still valid and has the address you're shipping to, guys on here overthink the transport of firearms as if there are LEO's just waiting to stop them on the way to UPS or FEDEX, by the way Buds Gun Shop offers a discounted service for shipping firearms that most likely will be cheaper especially a handgun which has to go second day.  Long guns can be shipped USPS

Firearms have to be taken directly to a shipping hub by a non FFL, no call tags.

Tell that to FedEx, who happily showed up on my front doorstep to accept my shipment of a handgun (declared as such), heading back to Springfield Armory.

And it's not that I'm overthinking anything.  Tom specifically asked what was legal, supportable by cited statutes - which is a polite way of saying, "please state verifiable and provable facts, not your own personal opinion of what the law SHOULD be".

If I wanted to be confrontational about it, I'd ask you to point out exactly which part of 2C:39-6f exempts 2C:39-5b (unlawful possession of a handgun without possessing a permit to carry) when you are transporting the handgun from home to UPS for the purposes of selling it to another party.