The reaction is this:
The only idea I have thus far is if we have a chloride acid that can form an ester, then we might be able to find a suitable mechanism. This would require a chloride reagent.
I have drawn a mechanism but I haven't checked for any references as I am at home now, so it's more like paper chemistry. The chlorine atoms should play some role and possibly disfavour formation of certain carbocations that you would expect in a standard Wagner - Meerwein. It is possible to draw a concerted mechanism (not shown here) but seems very unlikely
**EDIT: I have changed my initial mechanism so it explains better the methyl ester formation (see the comments below). The stereochemistry at C* has also been corrected.
As a general comment you cannot propose a non trivial mechanism without drawing one, it is handwaving. So I did.
I haven't looked at the literature either, but it seems to go like this: