First, they have an issue to take care of.

"Oh, crap!" Izuku said, slapping his palm to his forehead as a realization struck him.

"What is it, Master?" Momo blinked.

"The missing person's report!" Izuku said. "We need to get you back to your place, pronto! And... How exactly are we going to explain that?" he asked, gesturing to her misty tail.

"Oh, I see!" Momo smiled. "Not a problem, with your permission, I can simply reform my legs! I wouldn't be much of a sex **** if you couldn't access my pussy and ass, would I?" Ignoring his renewed blush, she continued, "This is the default setting when not in the lamp, outside of me having permission to have my feet, keeps me bound and close to the lamp," she added, tugging with her tail for emphasis. Izuku didn't feel the pull on the lamp in his hands. "...really gives me a thrilling feel of being helpless and owned," she admitted with a giggle.

"... thrilling?" Izuku asked.

"It's how genies are wired, Master," Momo replied. "Like I said, super submissive now. It gives me a lot of pleasure to be under another's control. My clothes are also easily changed back. I can go back home and explain that I came to this beach last night, and claim that I ended up falling asleep, which would be why I didn't return home. Assuming of course, you want to keep this whole thing secret?" She didn't even bother to mention that she could just erase the memory of her from her family and friends, as well as her registration into the census to ensure no obstacles between herself and her new Master. She knew without a doubt that he would never go for that option.

"Go ahead and reform your legs then. You have blanket permission to have them whenever you want them instead of the tail. Your clothes too," Izuku nodded frantically.

Momo immediately obliged, her tail disconnecting from the spout and coalescing into her legs once more. She then focused, and her harem outfit vanished, leaving her naked for a brief moment, smiling as she saw Izuku's face invent a new shade of red at the unobstructed peek, having done that deliberately. Her swimsuit, purse and belongings also reformed.

Izuku then realized All Might would be by at any moment, and wondered what to do with the lamp. "Can you hold onto this for now?" he asked, handing it to her.

Without thinking, she reflexively took it... And was promptly pulled down to the sandy ground like he had handed her a ten ton weight. "Oof!" she grunted.

"Ah, I'm sorry, what just happened?" he asked, helping her up.

"Probably should have mentioned, genies can't move their own lamps," Momo chuckled sheepishly as she demonstrated by grabbing the handle, and pulling with all her might. It didn't even budge. "Yeah, see? Another feature to show us our Master's power over us...."

"...so I guess I need to hold onto it," Izuku sighed, deciding he should probably hide it. While he trusted All Might, this was a huge secret that he would have to figure out if and how to tell him. Carrying the lamp might raise questions, hence why he had tried to send it with Momo.

"There a particular reason you can't simply come with?" Momo asked Izuku.

"Erm, well, I'm working with someone to clean up the beach," Izuku replied. "Both as a voluntary service to the community and as a training regimen."

"Oh, so you're the one clearing the beach up!" Momo grinned vibrantly as she brushed sand off herself. "I'll come see you as soon as the issue with me giving my family a heart attack gets cleared up!"

"Will you know where to find me?" he asked. She simply gestured to the lamp.

"I know where my lamp is at all times, just keep it on you!"

"Okay, good... Also, don't refer to me as Master when other people are around. My name's Izuku Midoriya, you can just call me Midoriya for now."

"Understood! See you later, Master!" Momo waved before heading off. Izuku quickly found a secluded spot on the beach he could memorize, dug up some sand, and buried the lamp for the time being.