Creating Thunderbird folders also creates them in Earthlink Webmail
I recently re-installed Thunderbird. When I create a new folder and move messages to it from my Inbox, the same folder is created in Earthlink Webmail and the messages also transfer to the new Webmail folder. Worse, the messages in the new folder disappear from Thunderbird. The net result is my Earthlink Webmail account is bulging and my Thunderbird messages are impermanent.
Opaite Mbohovái (2)
Have you tried subscribing to that folder? On clicking 'subscribe', it should appear in the list of folders.
As to the first part of your problem, that is how IMAP works: the same messages are in the same places on whatever device you use to access them, which includes web-mail.
As to them not showing up in Thunderbird I suspect David is correct.
Nde eikéke nde mba’etepe embohovái hag̃ua ñe’ẽmondo. Ikatúpa, emoñepyrũ peteĩ porandu, ndereguerekói gueteriramo nemba’ete.