can the apple id be found through the serial or phone number?

My sister had forgotten her apple id and at the moment her old iphone 5s had shut down completely. its still under warenty and when we went to apple they said they can give us a whole new phone. all we had to do was find the id and password in order to switch off find my iphone.. we've tried everything we have the bill to when she first got the phone er id and everything but its still alot. it would be great if we could simply find out the id and just answer her security questions.. please help