Use another window as video feed

We have a member of our congregation who joins our services here in UK from her home in Australia most weeks, through Zoom. She also leads parts of the service, prayers, readings and the talk fairly frequently.
It would reduce the amount of button pushing on the projector control if we could add the Zoom window (or any other window on the computer) as an optional input to the video stream background of a cue item, picking up both the picture and sound.