Problems receiving German characters in SMS
Android is Unicode-aware, and the native SMS app has no problems whatsoever in displaying German umlauts, regardless of the phone's language setting. 

The problem most likely sits with your network provider and is therefore outside your reach (unless you can easily switch providers after making sure the prospective provider offers better character support).

If you have data access, what you can easily do is use an alternative messaging app. None of the major apps like Whatsapp (the most popular in Germany, so your friend might already have it) or Viber should have problems with Unicode.