All Mail folder?

Hi there, we're new to mailbox.org, migrating away from Gmail. Im Gmail, there's the "All Mail" folder. Emails which get "archived" move from the Inbox into All Mail. It also includes all sent email. In mailbox.org I don't see an equivalent. However, I do want to keep the Gmail history by copying mails from Gmail to mailbox.org (via Thunderbird).

So my question would be: What do I do with the All Mail contents from Gmail? Where do I place those in mailbox.org?