You aren't going to need your original 'invoice'. newegg for example allows you to print your own invoice. They only ship you, a packing slip with your shipment.
As long as you regitser within 30 days with the cards serial #, they know you are the owner from that point on.
let me add, XFX asks you where you bought when you register. Along with that info, and your supplied serial#
they have the information they need.