Sure, download it to your local file system and then upload it to whichever
gallery you wish.

I did, but it uploaded to the 'Team Site' Gallery from Virtual Server Gallery but not to Web Part Page Gallery.
How do I upload .dwp file to "Web Part Page Gallery"?

Web part  Page gallery  doesn’t really exist, it is just the hidden web  parts that a user has closed that are available to be re-activated.

That may not be the technical answer, but it how it works.

It is not a manageable “gallery.”

Upload to the team site gallery and add it to pages from there.

Yes, you are correct. This is how it works.

Just to add my 2 cents... some people set up web  part pages that have a whole bunch of webparts that are available in the web part  page gallery  for users to turn on and off. If this is what you are trying to do - just close the webparts on the page  in question, and it will add them to the web part page gallery, where another user can easily add them back to their own personal view of the page.

The problem with this approach is that the code still runs … so it slows things down.

I agree. You just hide the webpart when you close it.

I guess closing a web  part is not a good thing to do. I have seen end users close a web part  and then wondering how to get is back. Then they drag and drop similar web part finally ending up with many entries of the same web part in the page.

Add the Web Part to the page  and then close it.

Web Parts should only be closed if you are
attempting to preserve personalization.