Which document must accompany the barber license and include a photograph?

The duplicate certificate is the correct choice because it is specifically a document that provides a replacement for the original barber license when it has been lost, stolen, or destroyed. This document must include a photograph to verify the identity of the license holder, ensuring that proper identification is maintained alongside the licensing information.

In the context of barber licensing regulations, having a photograph on the duplicate certificate serves as an essential security measure, preventing fraudulent use of the license. The other options do not typically serve the same function as the duplicate certificate. The training certificate is usually evidence of completing a barbering program but does not require a photo. An operating permit relates more to the establishment where the barber works rather than to the individual barber's licensing status. A student ID is relevant to those still in training and is not part of the formal licensing documentation required after completing barber training.