You're required to adhere to the regulations of the state that your vehicle is registered in. Just like how several states require front license plates on vehicles, but as I'm registered in Arizona that doesn't require the front plate, I don't need the front if I travel to one of those states. That said, if an officer is looking for excuses, that COULD be used as probable cause to pull you over (and as such, Arizona will provide a legal front plate if requested).
In your case, I'd base it on whether the rear of the camper overhangs the bumper enough to obscure the view of your plate. If it does, move it to the camper. Otherwise, leave it on the truck. Such as with my Amerigo - it's 11.5 feet long, and drops down over the rear of the bed by several inches. If I had it on a regular truck, it would block at least half of the plate, and I'd want to move it to the camper. As it is now though, between my flat bed, and deep drop rear bumper, it sits high enough that the plate isn't blocked, and I leave it on the truck. Same as with my Six-Pack camper. It's only 6.5 feet long (not counting the cabover section), and has zero overhang (if I didn't have the bedliner in the truck, I could actually close the tailgate with the camper loaded), so I leave the plate on the truck with that one as well.
What I used to do with my last Six-Pack that overhung the plate was request the 2nd front plate from the state, then left that one on the camper so I didn't have to remember to swap the plate back and forth when I loaded/unloaded the camper. Of course, you'll only want to do this if you always haul with the same truck....I don't, and had a lovely meeting with Officer Friendly at one point who thought I was pulling something shady with a plate on the camper that didn't match the truck I was hauling it with, lol.
1990 Ford F350 CCLB DRW 7.3 4x4
1990 Lance LC980 truck camper