in the state of Arizona
, you technically have up to 2 years
from the date of the incident to file a claim. While I would not recommend waiting that long, the point is that you are still well within the window to have your insurance cover the other vehicle's damage. The right thing to do is leave a note, when you see the vehicle again, with your contact info so you can coordinate with the owner of the damaged vehicle on covering the repair. A quick call to your insurance company once you've spoke with the other driver should get the ball rolling. Or you could always pay for the damage out of pocket.