Sounds like a dealer question to me. I doubt it's a theft-relevant part (especially since it looks like you are replacing it away from the dealer), but I hear you on maybe being VIN coded, and that I'm not sure.
Dealer should sort you for that inquiry tho, I would imagine.
I had my rear differential fail on my 2015 GLA45. Had it not been covered under my extended warranty it would have been an $6-8,000 dealer only job.
The dealer told me the the center differential is rear mounted and part of the rear differential assembly. This assembly utilizes a wet clutch system with a built in computer that required dealer specific programing to operate with the ECU.
So if the GLA250 uses the same system (less the AMG re-engineering), you may be forced to have the dealer source and install the required programming.
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