Hairy Scot,
I'm a little vague here because I don't generally need to convert ebooks, but I believe you might need to double check your Preferences>Conversion>Output settings. It sounds like you might have told calibre not to include book cover images inside your preferred format when it converts books.
The ebooks that already include covers in Moon+ are probably already in your preferred output format, within calibre's library - so no conversion is needed.
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