shower cartridge removal

Need help for my grandfather. He needs to replace moen shower cartridge, but the piece you pull on broke. He tried to screw in another screw and use that as leverage to pull the cartridge out, but that also didnt work. See attached picture. Any advice??

This is my first post for any kind of DIY so i hope i put all the info needed in here. The shower knob is NOT turning off the water in the shower now (so i turned the water off to the whole house). i am in a Lennar home (shitty builder) and they stripped the screw they put in the shower knob...

So the hot water in only my upstairs shower barely trickles hot water out. After a little research I found it to be just replacing a cartridge. When I got to removing the cartridge I hit a snag. Their was no locking clip only a locking nut/metal cover, that I took off but the cartridge wont move...

Not sure how to get this baby out. It seems the threads are in the way of the nut? The cold side came out like butta. Stuck hot side: Working cold side:

I went to replace the cartridge on a 20+ year old single handle shower faucet and I am now faced with what you see in the picture after removing the handle and trim. Note: I had to cut the handle off since it was stuck on, so the end is about 1/4 inch shorter than normal. There is no 'pin' to...