I went to my local mom and pop auto store earlier today for some non detergent oil for something and figured I better pick up some tranny fluid while I was at it. Did not see any type F but they did have type FA. I inquired with the owner if FA is the same stuff as F (figured it was but better safe than sorry).
We started talking and he was saying that if you have a newly rebuilt transmission then you can use the type III fluid because the seals and clutch material from a recent rebuild are of the newer more modern standards.
I just picked up a qt of type FA. I sure am not going to be the one to see if there would any trouble if you use type III and I for sure am not going to mix type F with III.