Mails from Local Folder can only be moved one by one


I am moving mails from my local folder to an IMAP account.
That worked well for more recent mails. But from one point in history onwards, I get the Error:
“The Mail with the Topic “xxx” and Date yyy in LocalFolder/Sent was not fully downloaded and for that reason it cannot moved to a folder of a different Account” (translated from German).

How can I fix this?
If I move this mail alone, it works - I suppose once I click that one mail, it IS properly loaded and then the transfer works…