There's a "Download all Private Messages as" link at the very bottom of the page for XML, CSV, and Text (I advise grabbing a copy in all three options, just in case).
Alternatively, you can just pick the ones you want to keep by using the Selected Messages dropdown menu and picking one of the Download As options, which would probably be more useful if you're intending to periodically clear them out and don't want to keep re-grabbing ones you've already gotten.
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