You are both correct and not correct. The H42 is the standard 4 speed and was used in both the 40 and the 60. In the later years of the 60 it got longer so that it was the same length as a 5 speed, but the one I have is the short one for a 40. I have one of each but I am only offering you for free the one that I just took out of my 40.
I also have a set complete of 3.73 diffs ready to drop in, but they would not be free, and they would not be available until after I sell my 60 so that I know I will never need them again. Down the road, when you have funds, we could talk about those.
But for now, the tranny is yours if you decide you want it. You would need to find a bell housing that would work as the 3 speed one does not match up. Wow, its a lot of work trying to give something away. I had to pay for a rebuildable transmission.
Sascha Steinway TLCA # 20217
1977 FJ40 "Ripper" (because it shreads!)
1988 FJ62 "Dino" OME, now in the hands of my daughter
2013 F-150 "Black Ops"