A TRACON Handoff/Assist controller reported the Radar Controller vectored a departing aircraft below the Minimum Vectoring Altitude.

Narrative

I was working the Radar Assist Position at Location A sector. I released an IFR departure (Aircraft X) on the ZZZZZ Departure climbing to 4000 ft. The Radar Controller was busy with a recent runway change and sequencing the arrivals into a difficult runway operation. I did my best to let the controller know that I released an IFR departure off ZZZ. The aircraft departed on the wrong beacon code and I alerted the controller that the aircraft needed to be on XXXX beacon code as the aircraft was IFR. At ZZZ it is not uncommon for aircraft to call for their IFR beacon code and depart VFR to pickup their IFR flight plan in the air. The Controller Radar identified the aircraft after a few minutes due to the complexity of the sector at the time. The controller then turned the aircraft to a 360 heading to move them away from other traffic but failed to climb the aircraft. During this time as the Assist; I was coordinating with other aircraft on the ground at ZZZ awaiting their IFR departures while trying to keep my eyes on the scope. Once I realized Aircraft X was northbound at 4000 ft. in an MVA of 6000 ft. it was too late and I told the controller to turn and climb the aircraft away from the terrain. The Low Altitude alert went off; and the controller never gave the Low Altitude Alert phraseology as he felt the turn and climb was sufficient to get the aircraft away from the terrain while dealing the rest of the sector at the time. He told me that he thought the aircraft departed VFR and was looking for the IFR clearance in the air. Obviously there was a communication breakdown and we weren't on the same page. The assist holds to right to release IFR departures off ZZZ; and it is customary to let the Radar Controller know that you have released an IFR departure off a satellite airport. If there was any change that needs to happen; it would be that the assist would change the radar tag to VFR if aircraft who depart VFR to eliminate any confusion on the status of the flight.