Putting messages back on a POP3 server
"Tools → Account Settings → Server Settings → Leave Messages On Server" controls whether a copy of the message is left on the POP3 server after Thunderbird downloads a new message. If you check this setting you will still be able to read the message from webmail after reading the message in Thunderbird. It's disabled by default.
This can cause a problem if you didn't notice the setting. If you want to put a copy of your messages back on the POP3 server so that you can see them from webmail, you could forward the messages to yourself. However, that would add new headers. A better solution is installing the Mailredirect Extension and using it to redirect the messages to yourself. That essentially forwards the message while making all of the important headers look like the headers in the original message.
The extension adds a redirect command to the Message menu (not the the Tools menu). You can also redirect a message by right clicking on either the message body or the message in the folder listing, and then selecting "redirect" from the context menu.
See Updating add-ons if you need to bypass the version check to install the extension. It also explains how to completely disable version checking, and the trade offs of doing that.
- Mozillazine forum thread where a user reports the redirection doesn't work with AOL accounts.