You are correct that the website is unclear regarding the origin of the puzzle car, although I have my doubts that a coachbuilder would feature the work of another coachbuilder on his website. Regardless of the origin, I really don't think that Grob's car and the puzzle car are one and the same. While they are very similar, I think I see too many discrepancies to indicate that they are the same car, even if we allow that alterations could have been made over some time span. Rather, I would speculate that perhaps Karosseriebau Wachtveitl produced more than one Austin-Healy Sprite conversion.
Alternately, perhaps one of the conversions was done by a second coachbuilder, who was inspired by the other conversion. Assuming this scenario, who knows which was the earlier, although somehow I think Grob's example looks a bit older.
