There is a way to replace a lost registration in BC, it's a bit involved but nothing too complicated or expensive. First thing you need is a completed bill of sale from the seller with the VIN and with that you can contact ICBC to search the system for the name of the last registered owner and try and get hold of them. If you can't get hold of them, you send a registered letter to their address and if it comes back unclaimed then you can apply for a new registration using the same VIN. I seem to recall that something needed to be notarized, might have been the bill or sale but it was a long time ago and can't remember exactly. If you can find an experience counterperson at a local ICBC insurance office they can guide you through it or there's a number you can call at their head office which deals with that. Another alternative is to get it roadworthy and register it in Alberta with a bill of sale then transfer it to BC. First method is probably simpler, though.