Get Gmail message to Thunderbird locally, and still leave a trace at Gmail

I seem to be able to find a way to satisfy my grave of keep my email offline, and yet able to keep my email easily searchable at Gmail. Here's what I did:

- Make sure in your ThunderBird Server Setting for each of your account, you leave the "Leave messages on server" checked with no other exception case checked.
- Get your email as usual.
- Once you are done, you go to your Gmail account, and you should see that all your messages are still there in the InBox. Select all message and ACHIEVE them instead of delete them.

At least this method works for me.