I think they will fit each other.
You are going to have a lot of prep work to get that copper stub ready to receive a brass ferrule for a new compression style valve.
I would get two new valves, compression or solder type doesn’t matter, that have that same football shaped handle and exact same configuration.
A multi-turn valve, not 1/4 turn.
As in, 1/2 inch copper to 3/8 compression, right angle.
Then it is extremely likely that you can just unscrew the big nut right behind the handle, and unscrew the whole guts inside the old shutoff, clean out any crud in the valve, and replace with the same part from a new valve.
When installing the new stem, leave it a little bit less than all the way turned in before tightening the big packing nut that holds everything in.
Otherwise it can bottom out too hard and break the plastic stem.
You can fully close the valve stem after the packing nut gets tight enough.
No need to make it super tight, just secure so no leaks.