They absolutely know. I had two phones delivered a week apart as one shipped from California & the other from China; the same driver delivered both, and commented on their contents without my saying a word. In fact, when the second arrived, he asked if something was wrong with the first one already!
Contact UPS. They weigh the package multiple times; that will help them figure out where in the delivery system it was swiped from the box.
This the thief wasn't smart, they should of put weight inside the box to make it impossible to trace. Call UPS have them look up where the weight changed.