If you seriously think the Last Main Mission quest to be really tough, then you are wrong, it is just like a piece of cake where you need to meet the Institute Leader called Father and he will guide you to Shaun and in return will ask you to join the Institute as well. Let's check out what happens in the Last Main Quest of the Fallout 4.
Now that the Transporter is ready to get going inside the Institute, go ahead and continue to get inside and search Shaun. Once you are transported to the Institute, exit the chamber and head east and you'll notice a voice will ask you to use the elevator and get down the Main Quest will begin.
As you step in the elevator, the door will be closed automatically and as you are heading down the voice which you are hearing will inform you that they already know why you are here and what are your purpose, they will also tell you more about the Institute. From one elevator, it's time to take the second elevator from the east from the corridor.
As the second elevator comes down to the end you need to head straight to the room and approach the boy behind the glass. The Boy is none other than Shaun, so convince him that you are looking for him from very long and also inform him that you are his Dad/Mom(the character you have chosen) and ask him to open the door. Once he refuses to approve your word he will ask you to go and talk to 'Father' and a Man approaches.
Try and interact with him to know about him more and ask where is Shaun. When the Man 'Father' reveals his true identity you are surprised and call him crazy, but when he offers you to join the Institute agree with him in order to uncover the complex future. So if you agree with him Father will ask you to go and have a meet with the Four Division leaders of the Institute: Clayton Holdren, Allie Filmore, Justin Ayo and Madison Li.
The first thing to do is return to the top and move south in order to take Shaun's terminal password from the office cabinet. Once you have the password head right and use the password to access Shaun’s Terminal. Now go from the east doorway head to the lowest level and meet Doctor Allie Fillmore. Convince her that you work with Institute now and know more about the Facilities Division.
Now get out of the Institute's central Hub and move towards the Bioscience lab to meet Doctor Holden and talk to him casually and once you are done with it just end the conversation and make note of the master-locked terminal from the north-end of the doorway.
Now keep following the Blue line towards the Advanced Systems lab to meet Doctor Madison Li. She will try to install a Courser Chip inside your Pip-Boy so that you can fast travel inside the Institute. Once you spot the final director behind the glass of the corridor, just keep following him and try to have a conversation with him as well. Tell him how you defeated the Courser and bring the current objective to close.
Now before you decide to leave the lab to make sure you explore the area very carefully. In fact you should explore the Institute whenever possible as it has many new things to explore and know. Now load the Holotape menu option and select the Network Scanner Tape to initiate the scan to complete the Main and the Final Story Quest in Fallout 4.
Note: If you select the 'Copy encrypted message' option then you will be sent back to the Railroad's 'Underground Undercover' faction as your current quest.
So make your decision very wise to play with which faction's loyalty first. Later the Fast travel option in the Institute will be available along with the next side quest Synth Retention to your Log as you agreed with Father to work for Institute and with this you start with Institute-based faction quests. From here you are all alone with the Side and the Faction Quest to be completed. Remember the Faction quest you choose will cause disturbance to your relationship with other Factions. Ultimately, you need to choose a faction to be with which will disclose the True Ending of Fallout 4.