I have a lot of messages stuck in "move messages" (notification at the bottom of the mail menu window. They are piling up

Hi NotInViborg,

We would love to help see if we can get to the bottom of what's happening. It sounds like you may have an IMAP email account set up. If that is the case, please see the information below for an explanation.

"If you have an IMAP account and are unable to move messages, it’s possible the messages contain invalid characters (typically added by a mail server) or are too large, or you exceeded the storage limits set by your email account provider."

If that isn't the case, let's try following the steps provided below from the same support reference.

"Move emails

1. In the Mail app on your Mac, select one or more messages.
2. Do one of the following:

• Drag the messages to a mailbox in the Mail sidebar or the Favorites bar.
• Click the Move To button in the Mail toolbar (you may need to first click the More Toolbar Items button), then choose a mailbox (or use the Touch Bar). Mail may suggest a mailbox based on where you’ve moved similar messages in the past.

If you move a message that’s part of an email conversation to another mailbox, it becomes a related message, but is still shown in the conversation. See View email conversations."

Reference: Move or copy emails between mailboxes in Mail on Mac - Apple Support

Cheers!