The back cover is detected using a magnetic field sensor - no magnet, no back cover, no memory card.

The state of the camera cover is detected using some type of light sensor - as the door opens iit slides a (highly reflective?) white patch in front of a sensor. When this patch is removed the door is considered closed.

I guess the Mugen battery has the white patch, so the device thinks the door is permanently open, but it has no magnet, so it never knows the case is attached! Not sure why the flashlight doesn't work in this situation, though.

I suppose you could add your own magnet by gluing part of a fridge magnet inside the Mugen cover, which should work - there must be plenty of room! Although it may end up being too far away from the sensor to be detected, so gluing it permanently to the magnet sensor may be the only option.

Can't help thinking Mugen have done a terrible job on this product - the battery is way too big for ordinary people, and the cover they replaced wasn't just a simple hunk of plastic.