ZLC Air Traffic Controller reported receiving an aircraft from Approach Control at an altitude that is below the enroute MIA; resulting in the Controller issuing the aircraft a turn; climb and low altitude alert to get the aircraft in a safe MIA.

Narrative

While working sector 6 Big Sky Approach began handing an aircraft off the was northwest bound at 100. The aircraft's route almost imperceptibly passed from Big Sky airspace into mine and then to Helena approach. I didn't measure but the aircraft may have been in my airspace for 1/4-1/2 a mile. It is pretty commonplace for Big Sky to flash sector 06 the data block of aircraft going into HLN approach since it is a non radar facility. I thought that was the case here. Suddenly the aircraft pilot reported in my frequency heading right into a 114 MIA. I tried to turn the aircraft to 100 terrain to their east and immediately climbed them to 120. I then issued a low altitude alert to [that aircraft]. I received communication too late with the pilot and they entered the 114 MIA area. RecommendationNot sure of any recommendations; but we aren't made aware of or trained on what coordination procedures Big Sky has with HLN approach. Also approach control facilities have different MIA from the center for the same areas.