If I play a ( Live ) party and I want to move in a correspondence game, please don't kick me out from the Live game. With the bach button i should return to the Blitz...

@Filipski
Have you tried opening the link to the website twice, then going to the live site from one of them, while keeping the correspondence site open on the other. Then I think you could just go back and forth between the two windows without having to exit one to go to the other. Worth a try anyway. It works on my laptop. I don't know about other devices like tablets or phones.