That description really makes me think GermanWings, seeing that they will connect you and do offer Star Alliance Frequent Flyer points, but aren't formally a part of Star.
In theory that means one of Cologne-Bonn, Berlin, Stuttgart, Dortmund or Hanover, although the announcement that Lufthansa flights outside Frankfurt and Munich are to be transferred to them complicates that a bit and opens the possibility of Hamburg and Dusseldorf. My money would still be on Cologne-Bonn with Dusseldorf and Stuttgart as outside possibilities.