DA-42 Flight Instructor reported being unable to restart engine after shutting it down for training purposes. Returned to departure airport and landed uneventfully.

Narrative

During Multi-Engine training; left engine was shut down for training purposes. The correct engine restart procedure was followed and the engine failed to restart due to the prop not unfeathering. Multiple attempts at both a starter assisted start and an air start were made with no change in the feather condition of the prop. After these attempts; I made the decision to secure the left engine and proceed back to ZZZ. We made contact back with ZZZ Approach and requested direct to the airfield. A few moments later the Approach Controller offered us the straight in approach to Runway XX; which I accepted considering the winds were calm. We landed safely on Runway XX; cleared the runway at Taxiway 1. My decision making during the process was as follows; after multiple failed attempts at restarting the engine; I determined that the best course of action was to go ahead and secure the engine; given our higher altitude; and the favorable single engine performance of the Diamond DA-42. I elected to come straight back to ZZZ because I wanted the additional help of ZZZ air traffic control; as well as the long/wide runway at ZZZ.