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It ought to be doable, but definitely not just unbolting the existing 8.8" and bolting in the 10.25".
As tjc said, U-joints are different and the snout is probably longer, so you'll need to have your driveshaft shortened and a new yoke put on the back end.
The axle tubes are almost certainly larger diameter which would require new U-bolts and plates, although I'm guessing the new axle would fit to the springs OK (although I'm pretty sure the F-150 springs are narrower than the F-250/350 springs the axle was originally attached to).
I don't know if there'd be any impact on brake or e.brake operation. I'm sure it would be easy to get the brakes to function, but the proportioning may or may not work out well. It might need e.brake cables from the 10.25 (not sure there).
And I'm not sure if the '88 10.25 has the tone ring and sensor needed for the RABS, speedo and ECM of the '96 truck (I'm pretty sure a new enough 10.25" would work there, just don't know if '88 is new enough)
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