Hi there OwenMor08! I’d be happy to help with this today. First, if you have a physical SIM card slot on your mother’s new device, simply move the SIM into the new phone, or put the SIM into your phone so you can access the codes.
If you have an eSIM-only iPhone, first make sure you are connected to WiFi.
You can then follow these instructions from the Apple support article I will link after:
“You can activate your eSIM while you're setting up your iPhone if your carrier supports eSIM Carrier Activation or eSIM Quick Transfer. With eSIM Carrier Activation, your carrier assigns an eSIM to your iPhone when you purchase it. With eSIM Quick Transfer, you transfer the SIM from your previous iPhone to your new iPhone without contacting your carrier. With either method, to activate your eSIM during setup, turn on your iPhone and follow the instructions.”
If this isn’t working, read the article linked at the end of this message, or get in contact with your carrier. About eSIM on iPhone - Apple Support
have a wonderful day!