I don't think you can if the connection is made with POP (Post Office Protocol), which it appears to be how you are connecting.
If your email provider supports IMAP (Internet Message Access Protocol) it would be an easy process to restore those messages on the server.
To restore the messages using IMAP connection:
- Back up your email to be safe.
- Create the IMAP account in TBird.
- Do a little testing by sending/receiving a few emails to make sure it works.
- Select the messages you want to upload back to the server.
- Right-click the messages and choose to COPY the messages into the "Inbox" of the new IMAP account.
- You are done. The messages you put into the "Inbox" will be restored to your email server.
It will take a few minutes, to a few hours or more to complete the upload depending on your volume of email and connection speed. Most likely, it will be much faster than the old connection (POP).