When I first acquired the gun, the top jaw screw was a really horrible replacement, which sort of fit the threads in the cock, in a very wobbly manner. The top jaw is correctly styled, but has no engraving, so it is obviously a replacement. I suspect someone snapped the lock without a flint or hardwood wedge, chipping the tip of the frizzen, breaking the top jaw screw, the top jaw being subsequently lost.
I whittled out a tapered square bit of hardwood, and twisted it into the cock. Measured the threads. Put a piece of round stock in the lathe, and proceeded to cut the threads, trying the piece in the cock every few thousandths. When I had a really nice fit, I shaped the rest of the screw. I'd studied photos to get an idea of the appropriate shape. The little tit at the end of the thread is typical. After polishing and parting off, I case hardened the screw. Colour is a bit off, but I think in time it will blend in.