Chosen Solution

I purchased a new screen and moved my iphone’s original home button to keep the touch ID working and now the home button does not work. It works fine when it is placed back in the cracked screen, but does not work on the replacement screen.

It appears that the Home Button link flex (it runs underneath the screen back cover) is damaged. That would explain why your button works on the original screen. I would contact my screen supplier and ask for it to be exchanged under warranty.