1.
Has she forgotten her Apple ID?, Check your Apple ID via your email box, see this Apple article: If you forgot your Apple ID -> If you forgot your Apple ID email address or phone number - Apple Support
OR see -> Having trouble signing in? -> https://iforgot.apple.com/password/verify/appleid
See also -> If you can't connect or sign in to iCloud -> If you can't connect or sign in to iCloud - Apple Support
2.
You can help your mom, see -> Help a friend or family member as their account recovery contact -> Help a friend or family member as their account recovery contact - Apple Support (IN)
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Requirements to be a recovery contact
- Your device must be running iOS 15, iPadOS 15, or macOS Monterey or later.
- You must be over the age of 13.
- You need two-factor authentication turned on for your Apple ID.
- You need a passcode set up on your device.
An account recovery contact can help make sure that you always have access to your account, even if you forgot your Apple ID password or device passcode.
An account recovery contact is someone who can verify your identity and help you regain access to your account and all of your data if you ever get locked out.
See -> How to generate a recovery key -> How to generate a recovery key
FYI: Make a screenshot or write down the recovery key and keep it in a safe place.
If you still need help, get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)