Ah, who can forget the days of "job shop convertibles"?!
When GM (and everyone else) decided the buying public didn't want convertibles any longer, the avenue was opened for indenendent shops whacking the tops off of cars. The best known was right up in the Detroit area called ASC, which stood for American Sunroof Corporation. A search of that company might produce some help documenting their conversions; and this one,if yhey did it.
ASC actually did some good work, but even on their best days, none of these shops were up to standards of the manufacturer-- if you can believe that! In those days "fit-and-finish" wasn't on the top of the list.
More than likely,the Phoenix this person has is in fact very rare, and perhaps even just two of them made... nobody else probably wanted one.
This second year of this Phoenix design (the '79 4-door looked pretty much like the '80 2-door) was a pretty good selling little car. Especially the rather silly looking 4-door with the slanted back hatch-- now we know where the old AMC Gremlin dies went to!! Not really.
Hope this helps