Menu items (Move To, Copy To, Copy/Move To special) that appear in explorer context menu get their contents from the Copy Handler configuration - to be precise from the "Shortcuts" section.
Initially the shortcut section is empty in Copy Handler and so the menus are grayed out.
To show some entries there, you have to define the paths that should appear there. Go to the CH options dialog, find the "Shortcuts" section and double click the "Defined shortcuts' count" to open the dialog box where you can define the shortcuts. After adding some paths close the dialog and apply in the configuration dialog.
Now you should see the paths under Copy To/Move To menu items in explorer.