First off, this isn't legal advice - cause I'm not a lawyer... so take this as you will... I aint responsible for it
I believe that it is going to depend on a lot of factors, one of which is where you are from.
In NJ you need a FID and paperwork to "transfer" a weapon to someone.
If you are hunting with a borrowed gun it must be 'transferred in the field' - that is, the lending party must be present.
In order to own a firearm you need a FID (unless it was willed to you in which case you're not allowed to take it out of your home from what I read... there may be other exceptions... but this too is gray from what I read).
Now if you are from PA I don't know if you need a FID or all that paperwork to own or transfer it - so if you have a PA drivers license and a NJ non-resident hunting license you likely wouldn't be asked for a FID in the field.
If you are from NJ and borrowed the gun in PA and left directly from PA to the field in NJ with the gun in tow you may be able to just say you brought it straight from your relatives in PA....
Bottom line: It all appears gray to me. I doubt you would be asked to present a FID in the field - but this could happen, especially if you are traffic stopped etc on your way there.
My 0.02 - someone who knows more about this please chime in! I feel like I only confused myself
[soapbox mode engaged]
This just goes to show you how these laws that were put in place with the premise of keeping guns out of the hands of criminals only hurts us citizens who have NO MAL INTENT and only serves to turn US unwillingly and unknowingly into criminals.
[end soapbox mode]
p.s. - Welcome to the forum and good luck this season!