I’m not sure if I understand 100%, but if you just want to be able to stream his entire stream, I’d say get VLC (VideoLAN.org) and LiveStreamer (http://docs.livestreamer.io/install.html#windows-binaries)
Open a cmd prompt and type “livestreamer URL best” and it will open VLC with the best quality, then in OBS (https://obsproject.com/) you can add a window capture for the “inner” window of VLC.
Then all you have to do is change the scene to fit your needs… mini in the corner, fullscreen… etc
and of course this would be 100% free.