I'm in the middle of replacing a faucet in our house's bathroom. I found copper lines coming off of our shutoff valves and am not sure what to do with them. I bought replacement flexible lines (Similar to https://www.homedepot.com/p/Homewerks-Worldwide-Universal-Connector-Kit-x-20-in-Faucet-Supply-Line-Braided-Stainless-Steel-7223-20-38-5/203082359) to replace them, but the copper lines don't seem to want to move. I'm uncertain if they're soldered or not, as they were held in place by nuts before I removed them. I don't want to damage the shutoff valve though. What is the typical procedure for replacing such lines? Are they just held in place by pressure and can be remove by applying force? I noticed that the lines at the top of the sink leak water when a small pressure is applied to them, but they do not come out easily.
Angle stops are cheap. I would just replace the angle stops while you have everything open and be done with it. The angle stops don’t look to be in good shape anyway. Then you can get ones that match the threads in your flexible hoses.
It looks like someone tried to seal the copper pipe ends up to the compression ring into the faucet fitting with silicon sealer material. At one time this may have seemed like a quick hack to correct for a leak in these joints but it was a nasty hack at best.
Another thought after looking closer at the pictures it may be that the hack was more of trying to make the wrong product work for the application. Still an incredible hack though.
At the upper end of the copper pipe near the sink faucet connection you could just cut off the copper pipe with a hack saw or a hand operated tubing cutter. Since you are replacing the faucet anyway it should not be a problem if a stub of the copper pipe is left in the end of the discarded faucet.
Now that one end of the copper pipe is freed up you can move the pipe around some. Hopefully this will allow you to get the other end out of the faucet fitting while breaking loose the silicon sealer. Once you have the pipe removed you will want to try to scrape as much of the remaining silicon sealer away from the inside of the faucet fitting. Silicon can be a persistent material and it can be a pain to get it all to come off.
If you bought the correct flex pipe coupler the ends should thread right onto the lower shut off valve and the new faucet.
Disconnect the faucet from the countertop if you have to. To break (what had better be just) the scale holding it place, tap lightly on everything in random directions, spin the pipe some, and pull it out.
That kinda looks like a blob of solder on the front of the pipe in the second image. Proceed at your own can of worms. Worst case scenario (within reason) is needing a new valve and faucet.