And while it fits perfectly, it will not moved with the kids 4 actor.

It should definitely move with the character if you followed all the steps to create the conformer. Before you do it again, there IS a possiblity that you didn't drop it over the character when you pulled it into the scene from the library.  So let's double-check that it is conformed.  Select the shirt, and choose Figure > Conform To. If it is in fact conformed, then it should show that it's conformed to The Kids 4.

If it's not conformed it will say "None."  So then you'll need to click the Down arrow and choose The Kids 4.