Thank you very much, tim.kramarz, for the file and for using iCloud.
I switched one Pose Morph to Animation. The other one was set to it already.
I used a Point Cache Tag on the object with the Pose Morph. After that was cached, I disabled the Skin and Pose Morph. I did this with both objects.
I deleted the PoseMoprhs, as well as the Pose Morphs related objects. So only object under the T-Pose Null stayed.
No problems after that.
All the best