I would clean the crap out of the parts, maybe even gently scuff up the surfaces, then splooge a high grade epoxy into the slot of the broken piece, prior to slipping into place. Maybe even epoxy a piece of safety wire around the perimeter to help retain the shape. Good epoxy should keep it there without further problem. You could also get some fiber mesh and embed it in epoxy smeared on the visible surface to build further integrity. I would be wary of drilling holes in the plastic and putting a screw in there. The plastic is already brittle from heat and age, adding a screw could potentially crack the plastic in a new place. Really really stupid of BMW to make this part out of plastic. I bet the replacement part is an assembly with shaft.