Currently, after a conversation was removed from Quick Chat and opened in the regular Chat window, there is no easy way to have it back in the Quick Chat. One has to close the Chat window and wait for the next message from the remote to arrive. This is inconvenient.
Hence I propose a button to send the conversation back into the Quick Chat. I propose a Down-Right-Arrow (i.e. arrow from the upper left corner pointing towards the lower right one) with the tooltip: "Minise to Quick Chat".
Will be an action, probably not enabled by default than you can add to the toolbar.