Itqualityassurance
What is Skype X?
Dear Skype, this (red X) button means close, not minimize. I also found the same question on the Skype website. Why would a company like Skype do something that is so different from the standard? Microsoft Lync (office communicator) also has this design of using X to minimize.
How do I start Skype for business minimized?
You can choose to have the Skype for Business window minimized to the notification area at the far-right of the task bar instead. In General options, under Application window, select the Minimize to the notification area instead of the task bar check box, and then click OK.
