If your device has been updated but still, you can't use screen share on FaceTime, you need to turn off FaceTime app and back on, check if the app you want to share supports the SharePlay service, or use iOS System Recovery tool to repair your iPhone after update.It's easy to enable screen share when you start FaceTime video call, and your music, TV show, movie will be sync with anyone joining SharePlay on the call.You can find the 'Share My Screen' option showing up on the right side during FaceTime calls following the iOS 15.1 update. SharePlay or screen share has been finally available in iOS 15.1 or later.
Problem of screen share not showing up in Facetime or being unable to use this feature could happen in iOS 15 update.