The emails are in different formats depending on the server, and it can be very complicated to migrate such as migrating a website.
The best and simple solution is this one explained hereafter
Once you've changed the DNS of your domain and point to us :
- Create same email accounts from your cPanel :
https://support.yoorshop.hosting/knowledgebase/5471/Create-email-account-in-cPanel.html- Configure your email software these new email accounts as pop or imap, following well the informations given in email account in cPanel, see the button 'Settings' or from cPanel V70 : 'Connected devices'
(Please do not change the settings of existing accounts mails in your email software with our settings, this will lose your emails)
3. From your email software, do a drag and drop of emails from the old account to the new account, and wait, this can take time depending on the volume ...
NB :
POP only store locally your emails
IMAP synchronizes emails in both ways : your computer-server