Most programs have a bit of leeway for people who find out about the program during a flight to get credit for it if they sign up soon enough after. Specifics vary. In this case, since you've already taken the flight, only the policies of UA and its Star Alliance partners matter. Check their Web sites and their forums on FT, focusing on those that serve the places you expect to fly from Japan and later from Toronto, to see which (if any) will give credit for flights taken up to 60 or more days ago. If you can get credit in more than one program, consider also the class of service and/or fare you usually expect to buy, since some programs are more heavily weighted toward high-fare travellers than others.