I have researched this axle swap in great detail for my truck and intend to do it at some future time. Here is what I have found.

To swap to a dually axle on that year F250 (and my '92 F350SRW as well), all you need is the Ford/Sterling/Visteon 10.25" DRW model axle from an '86-'97 F350 DRW pickup, as well as the wheels/tires. The DRW pickup axle with bolt straight up, as will the springs. Rear springs are the same length and width (3" wide) on the F250/350SRW/350DRW pickups in those years. It is best to get the whole axle complete, hub to hub, including the brakes and the springs. The duallys use slightly wider (1/2") and slightly larger diameter (1/8") brake drums and shoes.

Since your truck is 4wd, you will need to match the axle ratios of both front and rear axles. Factory stock axle ratio in these trucks was 3.55. 4.10 was optional on all F250-350 pickups, so the axle you find can have either ratio. There should be a tag attatched to one of the differential cover bolts stating the ratio. It can also be stamped into the cover. You can also count the teeth on the ring gear and pinion gear and divide to find the ratio. There is also a ratio code on the door jamb vehicle info sticker that states the ratio. I believe '39' is the code for a 3.55 ratio with an open differential. If there is a letter in the code, the differential is a limited slip. Numbers only, no letter is an open differential. I forget the code for 4.10.

The springs are also heavier to match the axle's increased capacity. The dually 10.25" axle is rated for 8250 lbs, versus 6250 lbs for the F250/350SRW model 10.25" axle. Springs are rated appropriately higher at 7500 lbs for the dually versus 6000 lbs for the F250/350SRW. Get the upper auxiliary overload spring setup from the dually while you're at it.

The rear sway bars are a little different too between the F250/350SRW pickups and F350 DRW pickups. Your F250 probly doesn't have the sway bar, so this would be a good time to add it from the dually donor truck.

Do not choose an F350 DRW chassis-cab as the donor truck because the chassis-cab axle is not wide enough and the spring pads and shock mounts are mounted in the wrong places to fit the pickup frame, due to the chassis-cabs having 34" frame rail spacing versus the pickup's 37" or somewhere thereabouts frame rail spacing.

Do not use a '99 or later truck as the donor truck either, unless you want to make the swap more complicated. The wheel bolt pattern is not the same (8 on 6.5" with 9/16" studs for the early trucks versus 8 on 170mm with metric studs for the later trucks). Frame rail spacing and axle width may also be different. The newer trucks' single rear wheel axles are wider than the older trucks. Not sure about the duallys. The newer trucks use rear disc brakes, which probly means also swapping the master cylinder and possibly brake booster. The discs would be a good improvement in braking though.

If you want to run the overloads, you will need to remove the overload spring bumper brackets from the donor truck's frame (grind off and punch out the rivets) and bolt them to your F250 frame (which should already have the holes) with regular grade 8 bolts or huck bolts.

To make it street legal with the duals, you will need to add the 3 red marker lights in the rear center below the tailgate and the 5 amber marker lights above the cab, as well as the amber and red marker lights on each side of the truck bed. Any vehicle over 80" wide must have the lights to be DOT legal.

You could run single rear wheels and tires on the dually axle to keep the width under 80", but you lose the additional capacity of the dual sets. You will still need a hub-centric type of wheel though, to use the dually hub as the support for the wheel.

The transfer case will be the Borg-Warner 13-56. It was used on all F250/350 old body trucks from the mid 80's through '97. Ford used the BW 13-42 on Broncos and F150's in those years. They stopped using New Process 203/205/208 transfer cases in the mid 80's, actually probly earlier than that for 203 and 205.