Yes as long as the current owner does not cancel it. New owner should inform their OPC to have the car registered once they have bought it. Quick call the the service department will do it.
Trade Purchase = No, and you will have to own the vehicle 3 months before it can be renewed on the vehicle, post a 111 check and rectifying any points raised.
Private Sale = Yes, of the remaining balance / expire date.
Bought a 2011 C4S from Ashgood Cars about a month ago and had no problem transferring the remaining 18months of the warranty. The car did have full OPCSH which I'm assuming makes it easier. Porsche Reading were really helpful, emailed me the forms, returned via email and a few days later got a letter confirming transfer and when my renewal was due. Also got the VTS tracking reactivated with Vodafone which was easy as well.
I bought my 997 from an OPC and not only did I get the 2 year used car warranty but I also had the remainder of the warranty from the previous owner which effectively gave me 2 years and 10 months warranty.