Liberty Reprimed

(For convenience's sake, bring Danse here as your companion)

After completing From Within or Outside the Wire, talk to Procter Ingram and follow her to the storage area. After explaining the main objective of the mission, you have to talk to Dr. Li aboard the Prydwen and convince her once more to continue repairing Liberty Prime. Once done, talk to Procter Ingram again.

Ingram will need you to build Electromagnetic Actuators. To do this, you have to get a High-powered Magnet. The quest will point you to a hospital where the magnet can be acquired. After getting the magnet, return to the Boston Airport and build the Actuators there.

The necessary materials should be quite common; and like Ingram said, you can get the materials in the airport. Build four actuators under the “Special” category in the build menu. Talk to Ingram again to update your objective.

Head to Waypoint Echo near the Edge of the Glowing Sea then talk to Scribe Haylen. After receiving the Distress Pulser from her, make your way to the Glowing Sea and find the Sentinel Site far southeast of the Glowing Sea.

Once inside the Sentinel Site, if you explored this location already, you can just take the elevator to the bottom floor then follow the tunnel back to reach the red door with the lift. Otherwise, check out this location's dedicated page for more info.

Once you've reached the end of the tunnel, you'll find a large red door. Enter through the white door above the stairs and broken terminal to reach the stockpile. Once inside, a Children of Atom cultist named Brother Henri will approach you. If you successfully talked your way in convincing him, you'll receive his terminal's password and you won't have to fight the nearby assaultron. Pick up the Cpt. Dunleavy's holotape in the nearby table as well. Operate the terminal to open the heavy doors.

Mini-nuke in front of the heavy lifter

Head inside then plant the distress pulser on the lifter. There's also a mini-nuke near the heavy lifter. Once done, talk to Danse and he'll inform you to head back to the airport while he stands guard by the nukes. Report to Ingram then activate Liberty Prime. Once done, Ingram will talk to you and the quest will be complete. You have to report to Maxson for the next quest.