I'm sure it's a factory A/C because it uses the same vents as the 65/66 Mustang A/C. I checked Ebay for Mustang A/C parts and I found a complete setup for $895. Nobody has bid on it yet. I looked in the Mustang catalog and they have a complete setup for the same price brand new with more pieces included so maybe that's why there's no bids. I also found the evaporator only for $245. That has no bids either.
The 63 unit is probably harder to find than a Mustang unit but there are a lot less people restoring them so your market is very limited. I think you'd be lucky to get $300 for it.