Sorry if I wasn't clear, I'm not using the app that moves someone from Android to iOS. By the 'Move' function, I was referring to the command available in the Notes app (which seems to be designed for just one way movement, from Gmail to iCloud)
When you there enable the Notes checkbox for your G-Mail account, can you drag the notes to G-Mail in the sidebar of the Notes application? I don't have a G-Mail account, so I cannot test. Works for Yahoo for me.