We went through this awhile back, can't remember who or where though..

IIRC there was no consensus and it was recommended to enquire of a dealer

(although as most of us know the dealers aren't exactly wizards)

I got interested after jumping someone's car from my E350 via my trunk (boot) battery..

Wonder if one of those solar-trickle chargers that attaches to your windshield and plugs into your 12v port would work?

Edit: now I see your last photo, that you have the official MB charger... now it comes back to me, that was their advice, use our charger.

So you'd think they could tell you how.  Surprised it isn't made clear in the charger's documentation..