Looking at Fords body builder guide shows the F250/F350 SRW both have a 12500 lb conventional trailer ratings per OEM hitch.
https://www.fleet.ford.com/truckbbas/non-html/2009/vs_pdf/Ford_TowGuide_03_09_09.pdf Now in the same guide it says your truck has a 15600-16000 lb 5th wheel/GN tow ratings so we know the truck won't have any towing issues at that weigh.
Many folks with the older 3/4 and one ton trucks upgraded the low capacity OEM hitch for a full class 5 hitch like the Curt #15572 rated at 16000/15000 lb draw and 1600/1500 lb load.