A FIP female adapter is made for standard male threads.
Compression threads are totally different, even between manufacturers. That's why a sleeve puller is so nice to have with your tools. The tool will pull off an existing compression nut and sleeve, and then you can install the new stop onto the copper pipe. I just did one of these for a friend I hadn't seen in years from my home town. He had an old 5 gallon American Standard wall hung toilet from 1963 which needed the correct flapper so that it would flush. Someone had sold him a flapper for a 1.28 tank, which wasn't working at all. While I was at it, new tank bolts and tank to bowl washer. And then we turned off the water to the home and installed a new compression stop at the same time.
He also remembered being at Whistler Mountain with my family in 1969, eating at the lodge on top and having the prime minister of Canada come over and ask if he could use one of our chairs for his table. Pierre Trudeau
Now his son Justin is the prime minister.
My grandson Mason and me on the right in green. Just a few years ago at Blackcomb Whistler