Hi there,
Are you searching for the solution to backup AOL mail to Thunderbird? If yes, then you can use the help from following article, which provides the methods to convert AOL mail to Thunderbird manually. Please refer the link to get more information.
Visit:
http://www.datarecovery.institute/steps-to-import-aol-mail-to-thunderbird/
If you are not able to perform backup to Thunderbird then I would like to suggest one another solution also, it is named as
SysTools AOL Backup, which can export AOL mail to PST, EML, MSG, and MBOX file formats then we can export these files to Outlook, Windows Live Mail, and Thunderbird respectively.
Thanks & Regards