According to the Metal Gear Wiki (emphasis mine):
Liquid Ocelot, often referred to as simply Liquid, was the man formerly known as Revolver Ocelot whose mind was possessed by the persona of Liquid Snake.
However, I cannot find any information on when and how this happened and it does not become clear to me from the games itself either. Could somebody enlighten me?
WHEN:
In Metal Gear Solid 1, Revolver Ocelots hand was cut off by a cyborg ninja (Grey Fox), while fighting with Solid Snake. After the incident of Shadow Moses, Ocelot got hold of Liquids body (or at least his arm), which he used to replace his arm.
HOW:
This is not explained in Metal Gear Solid 2, but in Metal Gear Solid 4: Guns of the Patriots. I could write up what happened, but the Wiki explains it quite nicely:
Big Boss later revealed to Snake that Liquid "possessing" Ocelot was a planned ruse in order to fool the Patriots as means of lowering The Patriots' guard against him. Big Boss elaborated that Ocelot was able to use hypnosis, drugs, psychotherapy and nanomachines to transplant the personality of Liquid Snake onto himself.
Okay I’ve played all the games numerous times and I believe I can provide the correct answer.
Liquid possessed ocelot because ocelot had a combination of: Latent spiritual medium abilities from his father and the fact he had liquids still living flesh grafted into himself. Liquids nanomachines containing traces of his personality infected ocelot. Mgs2 clearly stated nanomachines could even affect memory so it’s not a stretch that they still held traces of Liquid.
He was definitely possessing Ocelot in mgs2 because that was the story, despite Kojima retconning everything in mgs4. In mgs2 there was no story written at that point for future games. Mgs4 tried retconning this because kojima was having trouble coming up with new directions for the story. In the intro for mgs5 Volgins zombie is literally riding a fire Pegasus, this is how out of ideas kojima was.
Ocelot's hand was cut off in the first game. He got a replacement from Liquid Snake's body grafted on.
That's the when. The how is never really explained to my knowledge. Since arms and hands don't contain minds or brains it becomes one of the many how-does-that-work moments in the second game. The least insane thought I've heard is that Liquid's ghost somehow came along for the ride.
