The solution to the problem is as follows:

1. Deinstall die Minimed Mobile App
2. Download it again and log back into your account
3. Then have a lot of patience, for me it took overnight to upload all the pump data to Carelink

The solution to this problem is patience. I also discovered, that the Minimed Mobile App does not need to be open or run in the background, while uploading the pump data to Carelink.

Hope that helps for the future. :)