You just have to forage for proof of passage. The Organiser will probably expect to see a till receipt from a convenience store or garage, or an ATM slip, something like that, for each control location. These are examples of things that hopefully will have the (correct) location and the (correct) date and time printed on them. If you can find somewhere with a rubber stamp, so much the better of course, but from what I've observed people don't usually waste time even asking for such a thing - just go for the quick'n'easy till slip option.
I assume a postcard finish means there will be no finish controller, so you would have to obtain proof of passage as above, then post your card with all PoP's to the Organiser at the address provided.