Realistically, a 2500lb camper is no issue for any F250, even if it exceeds the manufacturer's GVWR of the truck. It will be within the tire ratings, and any sag can be mitigated with suspension aids.
HOWEVER, the camper does *NOT* weigh 2500lbs. That is the bare empty no-option weight. After adding optional equipment, and all his camping gear, the camper will exceed 3000lbs and may weigh as much as 3500lbs.
At that point, your friend will need to be concerned with tire capacities. At 3500lbs, the truck's rear weight will be around 6500lbs, which is 500lbs over the combined weight rating of the rear tires.
Even at 3000lbs he will be right at the limit for the rear tires, which leaves *NO* capacity for a trailer's tongue weight.