Here is my experience with finding fluid for the rear diff.
BMW Part Number:
BMW OSP Synethetic differential oil / PN 83229407768 / Container: 55-Litre barrel.
So that didn't work.
BMW Expressly approved hypoid oils:
A page long list of European manufactures, but one particular stands out due to my BMW motorcycling days:
Now where to find? It isn't a normal North American import.
Well what do you know: Land Rover part number LRN7591 sold in individual quarts. And this is what I ended up buying at the local LR dealer.
LRN Fluid part numbers: