I'm guessing you are having difficulty with the photo ID verification test as you added people you don't really know, so their photo is unfamiliar to you.
Anyway, you might try this idea. I don't know if it will work for you or not.
When they show you the image of the friend, screen capture the friend image and cut it out to where it's just the 'friend' pic. Now search that image on Google images. They will let you search for a duplicate image. There is a chance the person's image and link to the Facebook page will pop up on Google. Some people don't have their Facebook profile blocked from Google search, others do. So there is a chance you can track down the person in this way. In this way you can identify that person.
In the future, you should consider keeping a file of friend avatars and names just in case this happens to you again.