How do I do that do I have to download the Elgato software on both pcs?
You only need the elgato software on the PC to which the HD60 is connected via usb.
Another question, why when I connect the Elgato to my laptop and PC is only an empty desktop picture displayed with my background and my taskbar?
You have to set in windows the HDMI cable as "duplicate" specify. You can set this at the bottom right. He currently recognizes the Elgato as the 2nd screen
OK
Can I still stream on obs from my laptop or do I have to use the Elgato software? I still have the whole of obs on my real pc
You should be able to use obs synonymous if OBS recognizes the video signal.
Ok can I somehow transfer the settings from my old obs and the scenes?
I don't get a picture on obs (laptop)
Now I had to make a new scene with a video recording device
