After removing every weapon they could find from Stain's body, Momo created some rope for them to tie him up, before they started tending to Iida's injuries. Izuku has of course taken the most damage, but considering his ability to heal and inability to be affected by standard medicines, Iida was the priority.
Soon enough, although definitely quite late by most people's standards, the police arrived with the ambulance Izuku had called. The police were understandably shocked to see three teenagers carrying the hogtied body of the Hero Killer himself, and called for an armored transport to take him to Tartarus.
Iida was loaded onto the ambulance, and Izuku and Momo went with him, so he'd have company. The police also followed to the hospital to question them on what exactly had happened that night.
On the way to the hospital, Momo had some questions of her own for Izuku. "You knew something like this would happen, didn't you?" Izuku nodded as she continued, "You expected him to break your arm off, and that's why you asked me to make the new one for you in advance, right?" Another nod.
"I knew that Iida, with his speed, would likely find trouble within the next few days, assuming he decided to come to Hosu. I couldn't just leave him to find the Hero Killer, and die trying to defeat him, could I?" Momo sighed, knowing that no, he couldn't just leave Iida in the lurch, just like she couldn't leave Izuku and had to follow him here to protect him.
When they got to the hospital, all three of them were separated and questioned. Izuku truthfully told them that he had followed Iida here on a hunch that he would be getting in trouble, due to his recent circumstances, and had acted in both self-defense and defense of Iida, and later Momo, managing to defeat Stain in the process.
Momo explained that she had followed her friend Izuku, who she had a hunch would be getting into trouble, due to his phrasing earlier that day, and had acted in self defense and defense of Iida and Izuku, although Izuku was the one who managed to land the final blow to knock the villain out.
Iida insisted that the whole incident was his fault for seeking out the Hero Killer as vengeance for his brother, and that the other two had come to protect him, saving his life and taking down the villain in the process.
All of their stories lined up with each other's, so the police reached the decision that the heroes-in-training had two choices: Iida could, as he asked, take the blame for the incident, and would be at minimum suspended from the school for three weeks time, and one week for each of the others for not alerting their teachers or authorities first, along with a permanent mark on Iida's school record, although the three of them would take the credit for the capture of the villain.
Their other option would be to allow the credit to be handed to one of the heroes in the area with an electricity quirk, swear secrecy for the truth of the takedown, and none of them would be in severe trouble, at least with the police, although the school would be informed of what happened, if they chose to deliver additional punishments.
Needless to say the three of them took the second option, knowing that if they took the credit for breaking the law to take down a villain, they would likely get expelled anyways for unlicensed quirk use.
As for Iida, he would still need to stay at the hospital for the night, since he needed to recover his legs, along with the stab wound in his shoulder from when Stain first struck him, but the other two bid him goodnight and head home.
Izuku arrived at school the next day with his left sleeve tied at the elbow, his arm ending just past the shoulder. Noticing this, many of his classmates crowded him, demanding to know what had happened for him to lose an arm when he had both just the day before.
Izuku's only response was "It was a wild night last night."
After classes, Izuku was able to use his leftover crystal from his arm to finish the project he had been working on, and finished attaching the rest of it to the core he had left in his back. Elsewhere, Momo was able to do the same for her own side of the project, attaching the piece of crystal Izuku had left her to allow for his cells to take the arm over, before leaving it in the freezer to keep it stable.
Izuku needed his projects to be completed as soon as they could, since his opportunity to show his power at the Sports Festival was quickly approaching.