I just realized that I could test this myself and have. Even with 'Message Synchronizing -> Keep messages for this account on this computer', deleting from the server appears to delete the local copy.

Is there a way to get Thunderbird to retain the local copy if the copy on the server is deleted?

(Of course moving the local copy to a Thunderbird 'Local Folder' will prevent deletion, but I'd like to avoid this step).

If I delete a message on the server, will the local copy be retained?

No, An IMAP account synchronize folders so if you delete on server that will sync with pc.

You can look at your IMAP-PC-folders as views into those on server.

The "keep ..... pc" makes the whole message, instead of just the header, to be downloaded and so it can be read even when your not online.

You need to copy (or move) messages to a local folder to be sure its saved.

My question is why you have to delete on gmail but keep on pc.

I keep all messages from a few mailing lists (for reference, as one list does not have an archive). I may not want or need to keep all of this stuff in gmail (although extra space is quite inexpensive).

PS Gnospen thanks for the info.

I like to add sync goes both ways so deleting on pc deletes on server. https://support.mozilla.org/en-US/kb/imap-synchronization When you move to local the message disappear from inbox which then is synced with servers-inbox (deleting there)

BUT as deleting only marks the message to be deleted and not removes it, you must compact your folders. Then the message will be erased.