Recovery mails from Time Machine error while copying recovered mails to Mail folder

MacBook Pro - MacOS Monterey v12.6

Last week I've lost all my (4911) sent emails in a SMTP folder in Apple mail.

I tried to recover them by using Time Machine. Therefore I transferred, using Time Machine, the lost 'sent' folder to a desktopfolder and imported that recovered folder into Apple mail.

In Apple mail I see, 'on my Mac', the folder Imported, with the imported 'Sent' folder and its subfolders B7B7F6.... and further subfolders Data, etc.

When I click on the folder 'Sent', I can see all 4911 sent emails. So that's a good thing! But now it's just on my MacBook and I want them to recover in my SMTP folder.

But, when I try to copy these emails to another folder 'on my Mac' or the SMTP folder in Apple Mail, it does start the preparation of copying the 4911 mails, but in the next step, when actually copying starts, the amount of emails is decreasing to only 1335 emails. While copying I actually see the countdown happening from 4911 to 1335. Why is that happening?

So most of the 4911 emails can't be copied into other folders in Apple Mail. Not into folders ' on my Mac' and/or SMTP folders in Apple Mail. Also copying one-by-one isn't possible for some mails (mostly with attachments, I think?)

Can somebody help me recover all my 4911 mails into another folder, and preferably to my SMTP folder, so I can read all my mails from all my devices and not just my MacBook.

Thank you in advance,

Kind regards

Pieter