I'd check and see if the owner of the other half of the "Party Wall" was A, still around, and B, and if solvent sue for repairs.
Where are the all the experts that inspected the building prior to his purchase? Errors and Omission insurance maybe?
These party walls aren't rocket science, You tear down your building, you must now weatherproof the remaining now exposed wall.... It is settled common Law. A few hours at the court house/city hall should indentify the offender(s).
Drying out the exterior wall will raise its R value, Installing a layer of insulation would save thousands a year in HVAC costs...Maybe some program funds/grants loans are availiable, but probablely attached to regulatory maze and platoons of flappers.
Whisper "black Mold law suits" and that should motivate your lax friend to take action or sell the soon to be condemed building.
The sooner repairs are started, the less masonry will need to be replaced and or Tuck pointed, If the party wall is going to remain exposed for the forseeable future, why not upgrade the wall with windows to raise the value of the property while the scaffold is in place to resurface the wall?