Good news and bad news. The armrest is held on by screws on the back of the trim panel. Bad news is the hooks are molded and not individually replaceable. More people have broken these things off removing door trim than you could imagine. MBZ usually does a good job of designing things, but they really booted this one. Two options here, replace the panel, or find some way to engineer a repair. If... you have the broken piece, you can try reattaching it with some JB Weld. Really butter the broken piece and the area of the break on the door panel. Fill up the fillets between the ribs. Let it really set up well 24-48 hrs. If you're lucky it will stay together. This has worked on two occasions for me. There just doesn't seem to be any way to get those panels off w/o breaking at least one tab.
1987 BMW 325