The F100 Unibody in and around 1962 is a styling option where the bed is welded and smoothed to the cab. Underneath it has a frame. The unitized body trucks were built on the Econoline which uses a lot of Falcon parts.
The F100 used big truck engine options starting with the 223 inline 6, probably most were built with 292 Y blocks, these are different from FE/FT and MEL engines. For his 390, he'd need to use trannys/bellhousings for the FE/FT family which is 332, 352, 360, 361, 390, 406, the FE 410 (not to be confused with the MEL 410), 427, and 428. The early MEL 383, 410, 430 from 1958 into 1960 would work but Ford made a running change on the MEL's so after that they won't bolt without an adapter.