Getting the piece apart was really hard work The meshseams seemed to be glued to the rubber in the very first step. This ifixit- „knife“ did help loosening the seam. Again, the end caps: same issue the knife was neccessary to loosen the seems. Finally the battery: really stuck and swollen. Without the pencil-trick it would have been impossible: remove the four screws around the usb-interface and pull it out, move the flat band connector to the side and you see the bottom of the battery. Push with a pencil (dull end cap of the pencil, not the sharp end!) to the battery. I took a rubber hammer with delicate pounding to get to loosen the battery a bit, then put it on the edge of an old table so that the battery could move out and used the rubber hammer to nail the pencil into the bluetooth box to get the battery back out of the case.

Thanks for the tips!