Click on Share Screen then before you select the screen with the video, at the bottom left of the dialog you will find a checkbox titled, Share computer sound. Check the box. This will allow those seeing your shared screen to hear the sounds on your computer, including sounds from the video. (see the screen shot below)

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Does anyone have an update for this?  The screen no longer looks like J.B.'s response above. I can't find the Share Computer sound checkbox.

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