Welcome to the forum.
The F250 has 6100 RAWR/tire capacity and is good for around 3000 lb depending on the trucks actual scaled separate axle weights after its loaded and ready for the road.
The 8440 is most likely a dry weigh so add another 1500-1800 lbs for options and your "stuff" you add to the trailer. The trailer may weigh in the 10k-11k range which may mean a 2000-2200 lb pin weight which is well within the F250 load carrying ability.
How much towing performance the F250 has depends on the engine selection
I pull a 11200 lb 5th wheel trailer with a 2200 lb average pin weight with my 2500 Dodge/Cummins. Great combo