When he arrived back at the Midoriya household it was already dark outside, he passed through the door and saw Inko and Izuku watching a hero documentary. Inko looked at him and saw Momo hiding behind him.
Inko : Who is she? you should brough her back home her parent will worry for her.
Momo started tearing up a little a bit when she said those words but she gripped Murphy's clothes as if they were her last hope. Murphy then explained everything that happened and why she was here. At first Inko was furious that he broke apart a family but when she learnt that Momo's parents only view her as a tool and were far from what they show to the public she started pitying the little girl. But she was quite angry at Murphy because he showed the darkness of the world to a little girl that was having a peaceful life.
Inko : Its not because we suffered for one year that we need to make everybody else feel our suffering
Murphy : I just saw through the illusion they gave and their goal made me angry, i didnt though about it.
Inko : So what are doing now?
Murphy : We wait for the house I ask about to be bought then we move there
Izuku : But I don't want to live here, I have friends here
Murphy : Your so called "Friends" do they help you when you are getting bullied?
Inko : You are getting bullied, I knew it when I saw the marks on your shirt and on your wrist
Izuku : No im the one who protect them when they need it
Murphy : And you think its normal for them to rely on you when they have their own quirk while you are powerless
Izuku : But it's a hero job's.
Murphy : A hero first need the ability to protect himself before protecting others if not he is a fool.
Inko : Calm down both of you please
Izuku : Everyone can be a hero if they have the determination
Murphy : That's true but they first train to make their weakness disappear and then they fight for other. You are stronger than them dont let them beat you up because hero protect other. Heroes are respected by others not some pushovers.
Inko : Now its over both of you calm down! we are a family, no need to fight against each other. We need to find a way to live till the new house is ready.
Its was then decides that Momo will sleep with Inko and Murphy and Izuku will stay in their room. Two days later they were able to move in their new house. It was bigger their previous house, richly decorated. A note asking Murphy to dispel his clone was left on the door since each time Kirio and Izumi saw him they remembered they lost their daughter and even if they didn't feel anything about that, it make them remember that they have been played by a four years old and it maked them slowly go insane.
Inko didn't have a job anymore since she was absent for a year. To make money Murphy decided to make a websit where you could have access to movies, anime and music from his world internet. He didn't put every things since it could make people more dangerous and he still want to spit some rhymes someytimes. And that's how years later they became one of Japan's richest family. Inko decided to open a little restaurant near their house since she didnt want to keep staying at home doing nothing.
Izuku continued to go to the same school so he could continue his lessons with Stain, Momo was forced to go with him since she has a big brain quirk.
Murphy stopped going to school he only sent clones there. He wanted to develop his power before the start of the canon.
The first thing he tried is closing his eyes and feel everything through water, it was quite easy for him but when he moved it became harder, he developed it to its max extent, he was now able to see everything without using his eyes just by feeling the water in the atmosphere and in other's people body.
He then worked on his blade ( Tanto and dagger) mastery and developed his own style by basing himself on Cerulean's years of slaughter. His style was based on speed and efficiency.
He also worked on water bending since it was one of the most versatile style of bending. He was able to water bend, ice bend, cloud bend, blood bend and use his water for soul appeasing or destroying. He could also use his bending to heal any wound he wanted.
(water bending is too OP)
Nobody knew why but Momo grow really attached to Murphy and didn't want to leave his side but Murphy didn't care about her, he was obsessed with his strength (he is not dense he just don't want to make a move on a 5 year old). He taugh her an halberd art since it was her favorite weapon and she was able to produce it whenever she wanted.
At first Murphy wanted to teach all of them to use water related power but Inko refused she wanted to train herself to never be powerless again. He didn't ask Izuku since he knew that he will get quite the power up and quirks (sorry for those who dont read the manga). Momo wanted to but it wasn't possible since she already a power that had the potential of grow to a devine level.
At the end of his training Murphy was 15, he made himself look like a 15 years old version of himself because he couldn't take ladies pinching his cheeks on the street. But even in this body he still had too much charm but nobody would try to touch him since he always hide his the upper side of face with a blank mask. But his silhouette was enough to charm people.
He developed movement a technique that he called Frozen cloud steps that allow him to use the full potential of his divine body and go faster that the speed of sound. He could also fly by creating ice wings on his back or by forming and stepping on a cloud.
He decided that for his vengeance he will wait for the villain to attack U.A since nobody was able to find the villain base. It allow him more time to gain strength. Momo became able to fight against pro hero just with her halberd.
The government continue to monitor him but didn't knew of his progress but decided to ask him to go to U.A since they though that by being friend with other people his age who wanted to become hero, he could become like them and not be a constant menace for the nation.