I know the '51 Frazer uses the same control cable as the Henry J but I don't know if it connects the same way on the trans. It likely does. The Henry J has a bracket that's fastened to one of the trans bolts and the cable hooks into it and it clamps it up near the solenoid so it does not disconnect out the top. See (has a thin red box I drew around it) -
The way the actual cable connects to the lever is via that bolt through the lever on the transmission. That bolt has a hole in it and the cable is thread through that hole, then tighten the nut/bolt. It's hard to see in the upper picture but that's how it fastens.
Here's how the clamp holds it -