I don’t have any horse in this race, and I’m not interested in buying it myself, but it seems the best thing to do as a three-way conversation between the seller and the buyer and Purism to make sure everyone is on the same page and Purism is actually shipping the phone to the buyer?
Of course I can’t speak for Purism, and they don’t HAVE to get involved at all, but it certainly would go along way in making everyone happy and makes Purism look great by doing so from a customer relations standpoint, (going the extra mile when they absolutely have no reason to do so other than to make a new customer happy, and they could sure use some positive vibes in this area 
) but a simple transaction would have the buyer paying the $650 to Purism, then Purism refunding that amount to the seller, then converting the original sale over to the new buyer with their name, shipping address, other info etc.
Of course I’m sure the original buyer would have to acknowledge in someway to Purism, via electronic signature, etc., that they release Purism from all liability concerning the original sale.