Outlook 2007 how to get emails back to the mail server

So, Outlook popped out a message saying the inbox is almost full, so it need to auto-archive. Which it did. But, all the inbox is now available only on that Outlook PC, when I login into the mail server anywhere else (other PC, phone etc.) my inbox is empty.

So, PLEASE, how do I move the archived emails from being local only, to make them again accessible from any other device?