Is the car being represented as being completely original? Being a 1 owner car it shouldn't be too messed with but then again who knows, plenty of them were pretty severely modified even when pretty new.
I am not into restorations or original cars so about the only advice I would give is knew what you are getting, verify what you are being told and if something doesn't seem right, chances are they aren't. People are strange creatures especially when money is involved and even some of the best most honest can stretch the truth or omit relevant details.
If it is a 340 car, then look for the H in the VIN, check the engine, the displacement (340) is embossed on the side of the block. Ask a lot of questions and ask for any/all documentation. Take a lot of pictures as well especially if you do not seal the deal right away. To that point, its my experience that if you do not seal the deal pretty much right away, someone else will swoop in and get it. Just for fun, there are 4 locations of numbers; the VIN on the dash, the sticker in the drivers side door jam, on the radiator core support and on the drivers side of the cowl.
Lastly, I have no idea what they want for it but understand the value of the car before you go. Do not get "buck fever" and over pay just because its a Cuda. It might be nice but it isn't the only one out there. Everyone "thinks" they know what these cars are worth based on watching auctions and looking online but this is usually does not have a direct link to what that specific car is worth. Since you have experience buying/selling use the same techniques you have with everything else, this is not a unicorn.
Good luck