Sorry, I found the solution in another discussion:
"Crystal ask for DB Connections on new installation"
Correct Answer by Marc Trudel on Jan 9, 2014 6:57 PM ' Solved Reports are all saved with SQLNCLI which is Sql Native client 9 (2005) New computers only have SQLNCLI10 which is Sql Native Client 10 (2008) Customer will either install SQL CLient 10 on all old computer and upgrade the reports or install SQL Client 9 on new computers which will avoid upgrading hundred of reports
In my case the original Report was created on a System with both SQLNativeClient 9 and SQLNativeClient 10 on it. Because I originally used a SQL2000 database as datasource, the SQLNativeClient9 was used. It wasn't a Problem on the System when I dynamically connected to a SQL2008R" database, probably because the NativeClient9 was still there and could be used. On the other Computer only the NativeClient10 was existing and this caused the Problems.
But I think that this is a bug in Crystal: I think ist normal, that from time to time there are changes in DataBase Connections and Clients, so the reports should be able to work also with new Clients. At least there should be a message to inform about the Problem.