This seems like an oversight but there doesn't appear to be any way to refactor an inner class to be its own class. There is a "Extract Class..." option in the refactor menu which sounded promising but it appears to be aimed at extracting a handul of methods/members to be their own class. You can select the inner class to be extracted but it won't let you choose the same name for the extracted class as the inner class. Which is wrong because it won't share a name with the inner class after it is extracted.
Is there a refactor option somewhere that lets you extract an inner class to be its own class?