Greetings RJ! A Sport Fury convertible is a very desirable item these days, which increases the likelihood of its survival - provided it made it through the Sixties and Seventies. A lot of vehicles got crushed to support the Viet Nam war effort, so it’s very hard to say it your mother’s did, or not. And unless you have some specific paperwork - in particular, a VIN - it will be next to impossible to make that determination. DMV’s typically keep records for about 25 years or so, and there’s no guarantee the car even remains the same color. I wish I had better news.
Incidentally, I have a 1959 Sport Fury hardtop, and the owners also kept the dashplate - but, after I established contact with them, they sent it to me! You can read about it here.
If you have pictures of the car, I hope you will post them. And please let us know if you come across any additional information that might help us track down the vehicle.
Best
Dan