I think it’s done differently in Asia, his father wouldn’t technically be apart of his household even though they’re related. He would need to be added to his father’s household first (removing him from his mom’s household) and then have his father adopt Sungho..since his parents were either never married or divorced (it’s been a while, I don’t remember which), they would be considered separate households. Which in this case..would probably take longer, especially since his father doesn’t live in the country, and be counterproductive.
Correct me if I’m wrong.

He adopted him...why not ask his father to adopt sungho?