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Are you sure the person you're talking to isn't a bit thick, and is just seeing the display from their own camera? I mean, whenever I'm on Skype there's always a little window showing me what the other person is seeing. (Though I've never used the screen sharing stuff)
You can switch it off somehow, but I hate Skype and am not willing to fire it up to find out.
Edit: I hope for your sake I'm wrong, otherwise the other person will have wasted hours of your time purely because of their own silliness
Edit no. 2: I'm pretty sure there's no way to remove the image of yourself on mobile Skype, because I've tried it before. Maybe get them to turn their camera off and see if that does it.
I think the issue is that Skype for biz is just proper, proper shit.