First, thoroughly cleanse the iPhone as explained here:
What to do before you sell or give away your iPhone, iPad, or iPod touch - Apple Support
Then set up your iPhone (which will now look software-wise as if it just came out of the box) with your mom's information.
If her information is backed up somewhere (not in your computer's iTunes) under her Apple ID, it can be restored. If not, she would have to enter all her information from scratch.