How to login in game center without email adress using a name

Hi,

My daughter is using for game center login a name instead of her email address.

This is because of the former game center login possibilities.

Now we want to change to a new iPhone and for some reason I can't login anymore with her credentials.

I just don't know, did I forgot the right password or is it because of the name instead of an email address?

The difficult thing is, that - if I login with her email - it loads different game scores.

But we want the score from the game center account connect with this "username" shown below...

What can I do?