PA44 Flight Instructor reported landing safely with one engine operating after the other engine did not re-start following a training shutdown.

Narrative

Dual MEI lesson going as planned. Started heading back towards ZZZ1; while doing that we were practicing an engine fire in flight. Everything going as accordingly; shut down left engine intentionally. After finishing all our checklists; went to the unfeathering checklist. Got to Propeller full foward; with no reaction from our prop. Typically we see the properly move a bit; and start catching some air. This time we saw no reaction and propeller was completely still. Tried moving prop lever back to feather and forward; with no reaction. Crew elected to re secure and head to ZZZ; because of how close it was in proximity to us. Requested priority handling; and had a smooth descent and landing into ZZZ with no issues. Taxied and parked in the ramp area. After reflecting on the events; we have a couple thoughts on things that could have been better. One checklist item; which includes using the starter; at the end of the unfeathering procedure was omitted. I believe this was due to the startle and reaction to the abnormal behavior of the propeller. Instructor was focused on flying the aircraft; while SP (student pilot) had checklist items in hand. Student pilot wishes he communicated his thoughts on restart better to instructor to allow for a better decision to use starter since he was holding the checklist and saw the line item.