I did multiple things in parallel and finally it works:

• removed all Mails from the new MPB (~/Library/Mail/*)
• removed all preferences from the new MBP (~/Library/Preferences/com.apple.mail*)
• rebuilt the mailboxes on the old MBP
• copied everything once more
• after a restart, now it's working

I did multiple things in parallel and finally it works:

• removed all Mails from the new MBP (~/Library/Mail/*)
• removed all preferences from the new MBP (~/Library/Preferences/com.apple.mail*)
• rebuilt the mailboxes on the old MBP
• copied everything once more
• after a restart, now it's working