How to unlock: Complete Airship Down at the Boston Airport (M7,3).
- Talk to Father
The last main quest for the Institute is very short. After you see the explosion at the Boston Airport, access the world map and return to the Institute. After you get there, you need to go to Father's quarters for the last conversation. It does not matter which dialogue options you pick during the conversation. You will watch the final cutscene, but after it ends you will still be able to explore the wastes and complete quests (including completely new quests for the Institute).
Quest rewards: Experience points