I have an Adams #2 Fly press that I got a few years ago (second hand). When I got it I took it apart so I could thoroughly clean everything and inspect for any damage. I noticed right away that there is one tine ¼ - 20 screw is all that is left holding mystery part A that is attached to the main thread (with one Allen head screw that I cannot remove)  to mystery Part B that is attached to the ram with two push pins. Well when new both mystery parts A and B would thread together before you tightened the ¼ - 20 set screw. Well, over the years and previous owners the threading on both parts is gone so the only thing that holds the ram to the main thread is the ¼ - 20 set screw. Well now that no longer works and the ram drops free.

1.      Does anyone know how to fix the press without having to have a machinist remake both Mystery parts?

if you never want to take it apart again and just want to get more use out of it cheaply then check the nut you are pointing to in the first pic rotates, then lift the tool holder you are pointing to in the second picture, maybe put a block under it and let the press put the nut in place securely then weld the nut to the tool holder ( do not weld the nut to the threaded part above it as that has to rotate ).

to do a better job replace the nut and rethread the toolholder to a slightly larger size

Thanks a bunch for the advice! The small tack weld is a great idea.

I think that would do the trick!