The Battle of Bunker Hill Main Story, The Institute Quest
This quest will be triggered or can be aquired when you complete Synth Retention quest.
Related points of interest
Stages of "The Battle of Bunker Hill" quest
2. Reach Bunker Hill
I've been tasked with helping to recover synths that have escaped from the Institute and fled to Bunker Hill. There's a courser waiting for me just outside the settlement.
2.1. (Optional) Inform the Railroad
Available if you are a member of The Railroad.
Talk to Desdemona in Railroad HQ.
2.2. (Optional) Inform the Brotherhood
Available if you are a member of The Brotherhood of Steel.
Talk to Elder Maxson at The Prydwen.
3. Find the Escaped Synths
Working with a Courser from the Institute, I need to find the escaped synths hiding in Bunker Hill.
To get inside, you can use the rear entrance then open the hatch to the Utility Basement located behind the counter.
4. Deal With the Escaped Synths
We've found the escaped synths. Now to decide their fate.
You can reset them and send back to The Institute or set them free.
4.1. Kill the Courser
This stage is available only if you decided to set synths free or killed them.
5. Speak with Father in the ruins of CIT
I need to return to the Institute and tell Shaun what happened in Bunker Hill.
Father is waiting for you on the roof of the C.I.T. Ruins.
It doesn't matter if you freed the synths or sent them back, just during the conversation with Father tell him that you still want to be a part of The Institute and then you will receive next quest - Mankind-Redefined.
If you freed/killed the synths and told Father that you no longer want to be a member of The Institute then he will leave you and you won't be able to fast travel to The Institute anymore.
6. Quest completed
Next / new quest is Mankind-Redefined (Main Story, The Institute).