There are two ways of remove a program window from the screen without closing it. You can minimize window ore hide it. Minimized windows puts its buttons into taskbar. Hidden windows are invisible. Many applications use system tray icons (right and left corner of the screen) for opening of hidden windows. But you cannot put icon of standard application there.
If you prefer see your hidden program icon in the system tray you could use ActTray. After starting this program all other programs will hide into system tray instead minimize.
If you like it you can put this program into Windows Start Up menu.

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