The way Wolverine is portrayed is different than usual

Ami, Yumi, and Kaz was going to the new york orphanage to get a companion Kaz hates that saying they were inexperienced

Ami: Get it over it Kaz

Yumi: Yeah we are doing this and that's final

Orphanage manager: Hi welcome to the orphanage Puffy AmiYumi

Then Ami, Yumi, and Kaz walk inside and in the first room they saw a kid that had bone claws coming out of his fist asleep

Ami: who's that?

Orphanage manager: That's James Howlett

Yumi: We'll take him

Orphanage manager: okay I will bring him to ya outside

Ami: okay

then Ami, Yumi, and Kaz go outside

The Orphanage manager walks over to James and gently taps his shoulder for a second

James: Huh? let me guess nap time over

Orphanage manager: Your getting adopted James

James was happy he packed his stuff and brung it outside with him

Ami: James We are gonna be the best of friends

James then walked inside and set up his stuff in a empty room then he walked back into the main room

James: Hi who are you guys

Ami: I'm Ami Onkui and the purple hair Girl is Yumi Yoshimura while the old man that's wearing glasses is Kaz

James: I'm the age of 14

Ami: I'm 16 years old

Yumi: I'm 15 years old

Kaz: I'm 57 years old

if you want a description for Ami and Yumi look at the very end of a one-shot called Vs Lex on the whole hi Hi Puffy Sonic Multiverse one-shot collection and this is a one-shot collection happening