When starting Mozilla, if you only have one profile, both of the Offline preferences for startup mode ("Ask me if I want online or offline mode", or "Use my previous online/offline state") do not work. Mozilla will always start in online mode. To go offline, from the File menu, choose Work Offline.
*NOTE* Moving/Copying a downloaded message (while offline) will result in not being able to read the message at the new folder while you are offline.
'Workaround:' Go online to read it, and then re-download the message to have it accessible when you are offline.Credit: DSmithLady