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The guy that has it absoluetly right is Northeaster79.
See the 2wd beds are the same regardless of year. The only different frame widths were from the 73-77 F250 trucks. These had a narrow frame behind the cab, so these are the only interchange is between other F250's from 73 to 77.
Later trucks 78 / 9 4x4's and 4x2's will interchange. You can even take the 1/2 ton beds from early years and interchange with the 4x4 of the later ones, these will interchange. The exception here is the fuel fillers. Doors and caps can and will be different depending on location, and early trucks may not even offer a dual tank option. (highboy1975 mentioned this)
I think everyone was correct to some degree, it just has to be explained in a little more detail.
These bed swaps are common, and really a piece of cake.
The op's beds will interchange without mounting modification.
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