Just went through this. The cartridge came out, but the sleeve stayed inside the copper. After trying to work the sleeve away from the pipe walls with a flat head (and scoring up the copper in the process), I ended up having to cut out the valve and solder in a new one. A bit of a pain for a job I thought was going to take less than half an hour.
I was able to resolve this. The whole cartridge assembly inside the valve comes out easily, but you first have to rotate it a quarter turn (90 degress), after removing the retaining clip. There is a special tool for this included when you purchase a new cartridge. If anybody else is considering fixing the same type of faucet (Moen single handle), then I don't think there are any user serviceable parts on the inside, like rubber washers, so just consider replacing the cartridge. There are rubber washers on the inside .. But there are quite a few, and it's much easier to replace the whole cartridge than trying to find and replace the different washers/O-rings/rubber pads.
This just happened to us the sleeve staying inside the copper pipe. You will need a vice grip an and easy out! My husband worked on this job for about 3 hours, getting fustrated, finally got these two tools and the sleeve is out. Now I can look forward to a better saturday!
Call a plumber
I tried 90 degrees and still no luck getting the spool out? Any idea? Is it stuck, I'm pulling hard I'm afraid to break the copper pipes?
Sorry if I am not posting right. This is not an answer but rather a question. Anyway, I have a slightly different issue than what I have read above. I have managed to pull the cartridge out (by using a puller tool that screws into the valve stem and then sinch the large nut up against the end of the pipe). What happened next was the main part of the cartridge came out but the out sleeve still remains stuck inside. Any tips on how to remove? Without degrading the inside of the pipe making eternal leaks quite possible?