After two and a half weeks my phone came back and worked perfectly !!! There are 4 out of 5 stars.
They told me the first phone call that the repair service would send an estimate to ERGO Direkt. Were the repair costs have been higher than the value of the device, I would have only paid that amount to get (my phone was not even 2 months old). For this fear if I would do a losing proposition, because I buy a new phone, and thus a new insurance would have to complete, there is a star trigger!
I am quite satisfied with the progress of claims settlement!