Does the Volvo Factory Warranty carry over from a Private Seller?
 

My 02 V70XC transmission is on its last breath so I am looking at another Volvo.

THe Seller claims the car is still under factory warranty. Does that carry over to me?

Any idea on the process to make the transition?
Thanks in advance.

Yes.
Nothing needed to transition warranty but still a good idea to swing by the dealer with the car -
1) have them check it out, see what it needs etc
2) get the service history (from Volvo, independant garage work will not be shown, of course)
3) make sure recalls, service up to date

All car manufacturers allow the transfer of their NEW CAR warranties. Actually it may be a federal law. Make sure the owner gives you all service records and make sure they haven't done anything to void the warramty, like fail to have "recomended service completed" or had some mods installed to void the warranty. A dealer may be able to tell you. You can have any recalls dealt with after the fact. Also, you can register the car with Volvo on their website so they can notify you of any future recalls.