Hello Ken and Iñaki,
Now seems the auth is works fine and the user data is updated from the LDAP.
Currently im using FirsName, Surname and email.
The root cause was: I used the LDAP attributes what you suggested but I didn't set the "Update Local" and changed the "Update External"
Thank you very much again and I hope this topic will help others in the next time.
Gergely from Hungary