While stealing from the party is generally a good way to get them to do anything, honestly I doubt I would be invested enough in a free "very rare" item that was immediately stolen to even have stealing it be a real motivator.
I would try to track down the items, because it seems to be the plot hook. By about halfway through this all I'd be ready to quit, not because I've been deprived of a prized magic item, but because multiple "quest after something and it is a fake-out" scenarios is just a recipe for a terrible campaign. It's actually problematic for fiction in general but can be done well in a format with better control of pacing and controlling precisely what the audience knows about the story. TTRPGs are not the format.