I'm running iMac Retina 5K, 10.14.2

I'm assuming you have an imap mail account. If you have an Anti-Virus product scanning incoming mail/downloading of files, I suggest you switch it off, even if only temporarilly, to not cause any delays or interuptions.

You need to make sure you synchronise all folders to download full copies of emails for offline use.

• Right click on imap mail account in Folder Pane and select 'Settings'.
• select 'Synchronisation & storage'
• Select 'Keep messages in all folders for this account on this computer'
• click on 'Advanced..' button
• Make sure all your folders and subfolders have been selected - show a tick in checkbox - for download.
• click on OK

Under 'Disc Space'

• Select 'Synchronise all messages locally regardless of age'
• click on 'OK'

• Menu icon > File > Offline > select 'Download/Sync now'

Download and sycnhronise the following:

• select 'Mail Messages'
• select 'Work offline once downloaded and or synchronisation is complete'
• click on 'OK'

Once everything is synchronised and Thunderbird has gone into 'offline' mode: Highlight emails in batches. Right click on emails and select 'Copy to' and choose suitable folder in 'Local Folders' mail account. Repeat as required to get copies of emails.

I recommend using 'Copy to' rather than 'Move to' just in case something is not moved corectly and you lose an email. I recommend doing this in 'Offline' mode because it stops all folders synchronising with server whilst you are using those folders to get copies out of the imap account.

Offline mode is indicated in the bottom Status bar. On the far left, you will see a 'two black screen icon' when offline. Once you have finished, you can go back to online mode by clicking on the 'two black screen icon' and it will change to a 'two blue screen icon' when online.

If you can read emails in offline mode then you know you have downloaded full copies of emails.