You should probably talk to a lawyer about this some time. While it's true that in German and Austrian law, you cannot transfer copyright (Urheberrecht to be precise), any judge would simply ask the question what was meant by "assign my copyright". And it's very obvious that the owner wanted to give the Werknutzungsrecht (in Austria, Nutzungsrecht in Germany) to the recipient. And that's an unlimited exclusive license that effectively transfers all rights.
The only right one really cannot transfer is the right to claim authorship. So you may still say that you have written the thing, but you may not even use it without permission of the new rights holder.