Move Facetime session from iPhone SE to Apple TV 2nd does not work

I am logged in on the Apple TV with my Apple Account.

I start a Facetime session from an Invitation (I accepted) in my Agenda on my iPhone.

When I want to move the Facetime session to the Apple TV, I click on my name on the Apple TV. On my iPhone I receive a message to 'Move' the session to the Apple TV. When I click on the 'Move' button, nothing happens.

When I start a Facetime session on the Apple TV (logged in with my Apple Account) I can use the Camera and Mic on my iPhone to have this session.

What is the difference between the 2 and why is the first option not working?

I tried several other iPhones but not one is working.