Transfer bluetooth stick data?

My mom has a mouse that is wirelessly connected to a laptop with a USB stick. One part of the stick is broken, which is why she bought a new Bluetooth stick and wants the new stick to be compatible with the mouse. But how can you set up the new stick on this mouse? Do you have to chop the stick?

Is it a Bluetooth mouse or one with its own specific receiver? With the latter, a new Bluetooth receiver doesn't really help.

I guess the latter… I'll tell my mom, thank you