Sorry, the beginning of that post is a little garbled. Let's see if I can make it clearer:

1. 1. I am using Thunderbird with my ISP (Bestweb) on an IMAP server
2. 2. I use Thunderbird on two PC computers, mine and my husband's ("dh")
3. 3. I copied my TB profile from my computer to my dh's at the beginning of July.
4. 4. Both computers are set to "keep messages for this account on this computer" under the "synchronization and storage" account settings (see screen shot attached from my dh's computer)
5. 5. I keep all of my deleted items in a folder titled "Deleted Items". My account settings on both computer are never to delete these emails.

Well, it's a *little * better.  :-)

The bad news is that "keep messages for this account on this computer" doesn't really mean what many users assume it means.

With an IMAP connected account, the messages are stored on the server. To avoid internet traffic every time you view a message, Thunderbird can save a local cache copy which can be displayed almost immediately, rather than waiting for the message to be downloaded from the server. And that is what the setting to "keep messages for this account on this computer" means.

For a permanent copy, you really need to download the messages and store them somewhere detached from the IMAP-connected account, such as in Local Folders.

If you open Thunderbird offline, you should be shown the cached copies, and then you should be able to copy them to Local Folders.

But why on earth would you delete messages that you anticipate reading again? File them in an appropriate folder, please. I appreciate the "deleted items" folder may be one of your own making and is perhaps not equivalent to the regular Trash folder, but I don't understand the thinking behind keeping deleted messages, or naming a storage folder with the word "deleted". You may have told Thunderbird never to delete, but what about your email provider? Do they know that "deleted items" shouldn't be emptied?

Thank you for your reply and suggestions. I'm having trouble with this:

If you open Thunderbird offline, you should be shown the cached copies, and then you should be able to copy them to Local Folders.

I decided to try this with one of the emails on my husband's computer and it worked - I was able to copy it to a local folder. However, when I tried again (numerous times) with the other messages, no copy was made and I got a small pop-up window on the lower right that says "Thunderbird failed to connect to server queenmab@bestweb.net".  :-( Screen shot attached.

Here are the steps I followed:

1. Created a local folder on dh's computer titled "Recover Deleted Emails"
2. Position cursor on a message in "Deleted Items" folder on dh's computer.
3. Right click on message
4. Select "Copy To"/"Local Folders"/"Recover Deleted Emails".
5. After a minute or so, get message in attached screen shot

I honestly don't know what I did differently the first time it worked but I can't seem to make it happen again.  :-(

As for the name of the folder, that's just how my ISP handles emails that are deleted - it moves them to a folder titled "Deleted Items". They don't use a "Trash" folder and emails stay in the "Deleted Items" folder until you erase them. But, I never do - I just save them.

Thanks for your help.