How to repair connector on watch

You would need to desolder the bad connector from this screen, desolder the good connector from the donor screen and then solder it onto this one you're trying to repair. It's a bit of a tricky task and will require some specialized tools. Plus, this connector is made of plastic, so it can be difficult to transplant without melting, AND without doing any damage to the display.

I can't tell for sure from the picture, looks like there is some damage on the right side, but it's possible that all you need to replace is the little locking flap since it looks like that's the bulk of the issue. If that's the case, no soldering is necessary. Some magnification will help, but you can remove just the flap from the old connector and transplant it to the new one. That's a pretty generic Guide for ZIF type connectors, but the principle is the same.