But if by the case you mean the frame, it should be possible to have it replaced by the FP repair center, unfortunately paying out of pocket.
Please have a look at the FP4 price list.
Edited to say that now pictures are visible.
I find it impossible to assess the damage (I also don’t have FP4). There is a glimpse of hope that perhaps changing the back cover could suffice?
Depending on your location, you may try to reach out to some local Angels for assessment.