First of all I apologize for my bad English.
If a user opens for example an xlsx file with chrome he downloads it. From now on it is no longer connected to the uploaded xlsx file and changes will not saved. That's exactly not what I want Chrome to do. The file should be opened on the client with Excel and still connected to the file which was uploaded on the server. With IE it all works fine.
I've done some research and didn't find any solution which works for me. The OpenInClient feature is activated. Many thanks for your help.
Solution: There is no solution for this problem. Chrome can't handle files the way i want Chrome to handle. You need to use another browser (IE, Firefox, Opera etc.).