Forgot apple id
My mother’s iPhone has broken and can’t be opened.
The problem is that I gave her a new iPhone but she can’t remember the Apple ID
there is a way find it?
iPhone 5s
See: If you forgot your Apple ID https://support.apple.com/en-us/HT201354 and
If you forgot your Apple ID password https://support.apple.com/en-us/HT201487
You also can use Having trouble signing in/iForgot https://iforgot.apple.com/password/verify/appleid
And you undoubtedly will need to see If you forgot the answers to your Apple ID security questions https://support.apple.com/en-us/HT201485
Before trying to answer your security questions is very important that you think about your questions and their answers carefully and try to recall all details you can. If you don't answer them correctly enough, then you easily can lose control of your account.