Will Apple Care get cancelled if I remove the device from my Apple ID?

Hi! I’m hoping someone can answer this for me!

I just got a new phone and handed my old one down to my mom. We got it set up with her info and everything is good. I kept the apple care in my name because it cannot be transferred due to it being connected to my Apple ID billing.

Under my Apple ID in settings it’s still showing the 11 pro max, if I remove it will it cancel out the apple care on her phone? I do not want it to cancel!

I hope this makes sense. I am not tech savvy 😅

[Re-Titled by Moderator]