Re: "thousands of sent mail messages" : Help! Are my messages lost forever?
Wondering which Mac model, and which MacOS version you are using.
You. might want to check the Mail app's "Bin" / "Trash" and / or "Archive" folder to see if your recently deleted messages are all there ... if so, you can recover them. If not, it is possible they have been permanently deleted.
Depends on your settings where the deleted messages would go, or whether they've been permanently deleted:
Eg: In Mac OS Ventura: Use the Mailbox Behaviours pane to change where draft, sent, junk, deleted, and archived messages are stored.
If necessary, you could also search for a missing message: Search for emails in Mail on Mac – Apple Support
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Re: "message could not be moved to the mailbox" : "How do I stop this error message from popping up? "
Am no expert, so I could be wrong.
Seems your Mac needs to complete the task of moving all those deleted messages, and can not do so.
Wondering if the folder your deleted messages would go to is at full capacity (?), triggering the error message.
If so, guess you could keep emptying that folder for deleted messages, until all those deleted mail messages have completed moving there.