Morpheus is a program created by Neo and based upon the Real World Morpheus of Zion and Smith. 60 years after Neo's death, Morpheus joined the crew of the Mnemosyne and worked together with Bugs and the rest of her crew to help find and bring him back from the Matrix. After rescuing Neo, they all joined together based on a plan devised by Sati and rescued Trinity as well.
Following Neo's resurrection in the Analyst's version of the Matrix, Neo's doubts about the nature of the reality he was living in lead him to write a "Morpheus" program and set it inside a self-contained looping modal to let it evolve. If Neo's suspicions that he was inside a simulation proved correct, this program was supposed to come free him and lead him back to the Real World (much like the original Morpheus had done).
The program accepted Morpheus as his new name, but by his own assessment his personality was most likely based on two deeply formative figures in Neo's life: original Morpheus as Neo's ally and mentor, and Smith as Neo's crucial opponent. Morpheus the program described this internal personality conflict - combined with his existence in the endlessly repeating loop of the modal - as "more than a little crazy-making."
Morpheus would go on to realize that he was inside a computer program known as the Matrix, seeing its code in various locations, including a mirror. Seeing the code helped free his mind and open him up to the possibility of more in his life than just his basic programming.
Freeing Neo and Trinity
Acting as an Agent, Morpheus eventually found himself in the middle of an incident similar to one that Trinity had gone through over 60 years earlier. In the footsteps of former Agent Smith, Morpheus soon found a redpill named Bugs. The two briefly fought, ending with Bugs attempting to flee from the Agents. During the chase, Bugs hid behind the counter inside a key shop.
While she was hiding, Morpheus grabbed Bugs and rescued her, pulling her into a hallway of doors and leading her into Neo's old apartment during his time as Thomas A. Anderson. After discussing Neo and their own realization of what the Matrix was, Bugs gave Morpheus the choice between a blue pill and a red pill. He took the red pill and the two then fled the other Agents and escaped, leaping from a building and into the Real World. From there, the two joined together with the crew of the Mnemosyne to find Neo.
Morpheus and Bugs eventually found Neo, who had been living within the Matrix, unaware of his past. Morpheus and Bugs made an attempt to free Neo's mind, but he had doubted the possibility of the Matrix and fled. A gunfight ensued, with Morpheus taking out various Matrix security forces. During the fighting, Neo's boss came to the realization of his true identity, that of Smith. As Smith was about to kill Neo, the Analyst changed the scenery and brought Neo to him, attempting to make Neo believe that he had imagined the entire thing.
Neo later made his way atop a rooftop and to the ledge, with the mindset that he would fly, or fall. As he was about to step off the roof, Bugs grabbed him and pulled him back. She explained to him that he had done the same thing earlier, but didn't fall. Bugs had witnessed said event and it caused her mind to be freed. She later brought Neo through a portal that led from the rooftop to a train and then to a room where Morpheus, Berg and Lexy were waiting. Morpheus then used footage of Neo's first meeting with the Real World Morpheus to help remind him of his past with nostalgia. He then offered Neo a red pill, which Neo accepted. Soon after, the group was attacked and had to flee back through the portal into the train.
After a fight on the train, the group made their way to another portal to escape back into the Real World. Neo went first, awakening in a pod directly across from Trinity, who had yet to be freed. Neo was soon released from his cables and rescued by Cybebe and Octacles, who brought him to the Mnemosyne.
Returning to IO
Behind the Scenes
According to an interview with The Matrix Resurrections co-screenwriters David Mitchell and Aleksandar Hemon, the fact that Laurence Fishburne could not return for the fourth film had no effect on the story point in the released movie that the original human Morpheus died before its events. One of the original and core ideas for the fourth film was that sixty years passed in the real world, and the resulting emotional impact on Neo that almost everyone he knew is gone, even simply of old age. The new Morpheus-program made by Neo's subconscious memories was tentatively written with the option that Fishburne might even re-appear in the role, but he was unavailable, so they then followed their backup plan to simply cast a younger actor. Similarly, the presence or absence of Hugo Weaving did not affect the decision for Agent Smith to be revived in the fourth film: they hoped the original actor might be available, but he had a scheduling conflict, so a younger actor was cast as a new "shell" for the program.
The interview the co-screenwriters gave clarified that the Morpheus-program created by Neo's modal simulation was actually one of the first and core ideas that Lana Wachowski had for a sequel film: "She said she saw that opening scene in her mind in the middle of the night, one night in Chicago, and described it to me and to us. This modal little world which Thomas Anderson, Neo, has constructed for himself to be reminded of what he might have lost and what he used to be. Eventually, out of that world, the Morpheus comes." Essentially, Lana said that she was inspired to make a new Matrix film after the death of both of her parents right after each other, to deal with the grief. She then came up with the idea that in parallel to this, Neo had been resurrected by the Machines and plugged back into the Matrix, with his memory blocked, and so much time had passed that almost everyone he knew had died. But though Neo had seemingly lost everything, his memories of his dear departed mentor Morpheus would always be with him and always be part of him - subconsciously guiding him to create a modal-simulation based on his half-remembered dreams which ultimately allowed him to escape.
The name "Morpheus" is mythological name for the "lord of dreams", and now ironically the new "Morpheus" program originated as literally a dream, a creation of Neo's subconscious.
Morpheus's fate as revealed in The Matrix Resurrections slightly contradicts what happened to him in The Matrix Online MMORPG (2005-2009) - yet in broad strokes they are surprisingly similar. In both versions, Morpheus is actually killed in a violation of the Truce, but later a sentient program arises in the Matrix using Morpheus's old RSI (digital appearance), who allies with the humans.