Drag and drop a message from Gmail Inbox to your Local Folders account should be similar to deleting the message. Check this Gmail article to understand what that means. https://support.google.com/mail/answer/78755

If you don't need to see 'All Mail' in Thunderbird simple unsubscribe from it.

Thanks for reply. Its not that I do not need to see 'All Gmail' in TBird but I do not want to keep it in 'All Mail' at my web acct when I have moved it to the TBird Local Folders. Hence (presumably) I have a 'hard copy' on my pc and the web Gmail/All Mail is not required. (Note that I do copy all mails to an extHD each month so I have that copy to recall if ever needed).

You may consider backing up the entire Thunderbird profile (including all mail folders) on a regular basis, not just the mail folders. https://support.mozilla.org/en-US/kb/profiles-tb#w_backing-up-a-profile

There is nothing wrong with keeping 'All Mail' if you find it useful. And you'd need to delete the messages transferred to 'Local Folders' anyway.

For me it's somewhat redundant though.

Thanks. Yes, I do back up Profile etc each month and just to be sure I also use Mailstore to provide additional protection.

I simply did not realise that Gmail retains copies even when they are moved to TBird Local Folders ... I wrongly assumed I was 'dragging the mail' out of Gmail into TBird Local Folders (used WLM before TBird). Pity this is not some kind of 'auto' feature but in future I will make it a policy to delete the mail copy in All Mail since I don't need it held by Google.

Just found this thread: https://support.mozilla.org/en-US/questions/1117427

I think that this solves my problem ... copy mail to Local Folder and then delete at Gmail ... rather than dragging email to the Local Folder.

When your problem has been fixed can you mark the thread as 'Solved' please? Thank you.