Hi AQ27,
Thanks for using Apple Support Communities! I see you have a question about setting up your mom's new iPhone with her own Apple ID, but keeping some of the information, and I'd like to do what I can to help.
Since she has a new iPhone, is she planning on setting up with a backup using your Apple ID? If so, once the iCloud backup is finished loading, she can sign out of your Apple ID and she will be asked if she wants to keep a copy of some of the data on her iPhone. Items such as Contacts, Photos can kept on her iPhone, and will not affect your iPhone.
Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac
How to create a new Apple ID
She'll then sign in with her own Apple ID. Once she finishes signing in, have her make a new iCloud backup to be kept with her own Apple ID. Sign in with your Apple ID
Back up your iPhone, iPad, or iPod touch to iCloud
Some items which can not be saved from your Apple ID are Messages and iCloud backups.
Apps can also not be transferred to another Apple ID. She can go to the App Store and download the apps that she wants.
If she has purchased apps and wants to keep using them, Family Sharing is an option. You can read about that here: Family Sharing
If you want to set up her iPhone as new, with her own Apple ID, you can AirDrop the photos that she wants from your iPhone to hers. It's pretty simple, and quick, as it uses Wi-Fi with Bluetooth enabled. How to use AirDrop on your iPhone, iPad, or iPod touch
Take care!
