iPhone se2 home button Touch ID not working

See the options in this link, but the phone may have a hardware issue and if it does, it will need to be seen at the Apple Store Genius Bar for evaluation and options --> If Touch ID isn't working on your iPhone or iPad - Apple Support

Then buy a new iPhone. We are all users on this user to user only forum and we can't fix your mother's phone. And since Apple has evidently already evaluated the phone (something you should have mentioned in your first post), you'll have to do what Apple recommends.

Edit: I didn't even notice until I relooked at your photos that the Touch ID button is damaged. Clearly the phone sustained a fall, which damaged the button. The button is integrated into the screen. It can't be fixed or replaced, unless as part of the entire screen. I can now see why Apple recommended buying a new phone.