In principle, you can teach a repeater to different routers, but it must be reconnected to the respective router each time. There is no provision for automatic, mobile switching between several routers without having to set it up again.

This means that if you want to use the repeater at a different location (e.g. at your parents', holiday home or at home), you have to reconnect it to the router there and set it up again. The repeater only saves the connection for the router currently set up; parallel or automatic switching is not possible.