recovery of APple ID

Have you checked Settings on the phones to see if the ID shows anywhere such as Messages, FaceTime, iCloud...?

See if you can recover the ID/password. Use every email address you can think of.

Apple ID - How to find your Apple  -  An iCloud e-mail address is an Apple ID.

Apple ID - Find  -       

If you forgot the Apple ID (iCloud) password, enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option if necessary. Link to contact Apple Support at the end of the 2nd article.

Apple ID - Manage  -     

Apple ID – Forgot Password  *