I've thoroughly gone through the article on synchronizing messages on the server with messages stored locally on my machine.

With IMAP all messages are managed on the server. This is the way IMAP works, and there is no way around that. 'Synchronization' is Thunderbird speak for also storing an offline copy of all messages on the server on your local disk. It does not however move messages off of the server to your local disk, which is what you need for not exceeding the storage quota on the server.

The only thing stored locally is what was stored when I initially copied the Inbox (on the server) to Local.

You'll have to move messages off of the server to your Local Folders account. Note this will also remove them from the IMAP account. Before moving messages manually, make sure there is a local offline copy in your IMAP account, and you do have a recent backup of your Thunderbird profile folder. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile

This way you can restore messages if something goes wrong.

Alternatively you can use the Archive feature, and designate a folder underneath 'Local Folders' as the Archive folder for the IMAP account. https://support.mozilla.org/kb/archived-messages

Archiving does essentially do the same as moving messages manually, but in a more comfortable way.

Thanks. I understand IMAP, and deleting messages from the server manually is no problem. When I first copied everything to Local folder, it was all there, including my complex nested folders. But nothing that came in later would be there. So today I selected all the messages in my Mail Read folder that had not been moved, and did a Move. That put them into the Local folder and deleted them from the main one synced with the server. So I'm not clear if I can or should use this method. Can you help?

I found the profile but it lists only a small fraction of the complex nested folders spanning 2004-date. So could you help me make sense of that?

I looked at Archive, and I noticed that has an option to organize my the folder structure of the main account. If I want to be able to easily access old emails, this sounds like the right way to go. I don't just want a backup, I will frequently need to access old emails given the skimpy storage my mailhost provides. Am I starting to get this correct?

And my office manager has two accounts on her computer, one for her predecessor's emails, and one for hers. And I have finally bought her a new machine, so all this will need to be moved over to her new machine. Are there complications here I need to pay attention to?

Your help is much appreciated.

When I first copied everything to Local folder, it was all there, including my complex nested folders. But nothing that came in later would be there.

I'm not exactly sure what you're trying to say here. What you did was a single manual action, which you'd need to repeat at any time you want. There is no automation for this.

So today I selected all the messages in my Mail Read folder that had not been moved, and did a Move. That put them into the Local folder and deleted them from the main one synced with the server. So I'm not clear if I can or should use this method.

If freeing up space on the IMAP server and also keep the messages is what you're trying to achieve, then this is what you 'd need to do.

I found the profile but it lists only a small fraction of the complex nested folders spanning 2004-date. So could you help me make sense of that?

That sounds like a different problem, and you may want to start a new topic for this.

I looked at Archive, and I noticed that has an option to organize my the folder structure of the main account.

You can also designate a folder underneath Local Folders as the Archive folder for the IMAP account.

I don't just want a backup, I will frequently need to access old emails given the skimpy storage my mailhost provides.

Archiving messages in Thunderbird essentially means moving them into an Archive folder. So they'll remain perfectly accessible on your computer. But they won't be accessible anymore from another computer over the network. Archiving messages doesn't eliminate the need for profile backups.

I have finally bought her a new machine, so all this will need to be moved over to her new machine. Are there complications here I need to pay attention to?

Transfer the entire Thunderbird profile to the new computer. https://support.mozilla.org/en-US/kb/moving-thunderbird-data-to-a-new-computer

I had the same issue and, after a lot of searching, found a discussion on TOOLS - Message Filters. You can setup a message filter to automatically move messages from an IMAP server Inbox to the Local TB Inbox each time you check for new messages.

1. Open Yools - Messages Filters 2. Select the IMAP Account in the "Filters For" (at top) 3. Create a New Filter (right)

      a.  Give the Filter a name i.e. "Move All Messages"
      b.  Checkmark the "Manual Run" and "Getting New Mail"
      c.  Select  "Match All Messages"
      d.  Select "Move Message to"  and "Inbox on Local Folders"

It Kinda works, but sometimes I have to click on the IMAP Inbox, which forces Thunderbird to link to the server. When the server responds, the Filter moves all of the messages to your Inbox.