Keyboard shortcuts aren't woven into the help body text, but the last major heading in the Help file for most Adobe apps is "Keyboard shortcuts," and the shortcuts for screen mode are listed on this Photoshop Help page:
One more place to find shortcuts in Photoshop is the Edit > Keyboard Shortcuts command, where you can also change the shortcut if you want.
There is something unusual about the screen mode shortcut, though. Normally you can mouse over a tool or icon in Photoshop and the keyboard shortcut is shown in the tool tip, or listed next to the menu command. But for some reason, the View > Screen Mode menu item and the tool tip for the Screen Mode application bar icon do not list the F shortcut.