Migration emails between two servers

Hello,

We have a server with emails (Plesk Onyx). We must migrate all the accounts on a new server where is the website.
We use the imapsync soft.

The problem we have that we must activate "mail server" on Plesk Onyx on the domain on the new server.
And during the migration... emails generated by the website arrive on future accounts (on the new server).
And we want that emails generated by website continue to arrive on the server when the account are at this moment.

It seems that...

Migration emails between two servers