I'm Tak, Software engineer.

GitHub Transfer, Is a Very useful feature.
So you can easily transfer the repository to another account.

1. click "Settings" in GitHub repository
2. click "Transfer"
3. Select the new owner account
4. click "I understand, transfer this repository"

It's so easy.
In addition settings, wiki, and issues can be automatically transferred.
And of course, you can transfer forked repository.

But if the original repository is private, you can not transfer the forked repository.

You read the official document.
https://docs.github.com/en/repositories/creating-and-managing-repositories/transferring-a-repository

Oh...how do I transfer...

Don't worry, there is a solution.
First, you detach forked repository from private original, so you transfer repository.

You use GitHub Support.
https://support.github.com/request/fork

You select "detach forked".
Next, you contact GitHub Support.

The support ticket title is "Detach Fork".
The support ticket message is

In the below repository, I'd like to unfork and turn it into a standalone repository.
* https:// want to detach repository url
and I never merge to this repository.
* https:// original private ripojitory url

8 hours later,　GitHub Support detach repository.
But there is condition, so You have administrator role in original ripository Github account.
If you don't have administrator role, original ripository Github account administrator contact GitHub Support, so detach repository.

Finally, you can transfer repository.
It's a little tough.

But this article will help you.

Thanks to read this article.