A Center Controller reported they issued an IFR clearance to an aircraft to maintain an altitude below the Minimum IFR Altitude.

Narrative

Aircraft departed ZZZ VFR and called on XXX.XX to pick up his IFR flight plan; he filed for 8;000 in a mountainous area. There was an active MOA and known weather along his filed route; I tracked up the data block and no MSAW alert activated. ZZZ Approach Control also required a point out to facilitate his clearance. The pilot stated he could maintain his terrain and obstacle clearance in the climb and I cleared him 'as filed' at 8000. The MIA (Minimum IFR Altitude) in the area was 9000 but when I looked at it; it appeared to me to be 8000. There happened to be a lot of map clutter because of airspace boundaries; TFR's and weather. I then tried to change the aircraft; unsuccessfully to XXX.X as he was on the sector boundary between my sectors. After the aircraft cleared the Approach Control airspace; MSAW activated as he was leaving the area of higher terrain. No Llow Altitude Alert was given as the aircraft had already transited the terrain and was crossing the boundary to a lower MIA. No discussions of terrain occurred during the point out. I obviously messed up by not observing the correct MIA. I presume that no alert activated because the computer was calculating the Approach Control's; presumably; lower MVA in that area. This would explain the lack of concern by the Approach controller as well. The aircraft continued on without incident until he cancelled to be able to transit the MOA and remain north of the convective weather.I should have observed and fixed this problem; however; the MSAW alert activating after the fact didn't really have it's intended affect on the situation. Normally; it would activate after data block acquisition and before clearance issuance after radar identification.