I'm not German, but as far as I know they have similar system to the one we have in Poland - you can transfer exclusive financial copyrights to another entity but you cannot transfer personal copyrights (so that you can say that you are the author of particular work even if you cannot license it to 3rd parties). In practice, even though personal copyright is not transferable, many employers require you to sign additional civil contract in which you declare that you will never exercise your personal copyright.

In the granting of usage rights it is usually included that the employer will have exclusive usage rights as well (dependent on wording).

I don't know about the exact implications for creating very similar future work (what you would call "infringing copyright") though.