Before the transfer, you have to just "Pause" the stream in your original camera. Then go to YouTube studio and copy the streaming address and stream key from the already existing stream. And set up the new stream as described here: https://camstreamer.com/blog/how-to-set-up-youtube-via-rtmp-service. Remember that the new stream has to have exactly the same parameters (especially resolution) as the original stream.
Never STOP the stream in your original camera via stream settings as we would stop it on the server. You can uninstall CamStreamer App on the original camera and it will work from the second camera.