Hello Luciano,
welcome to the forums!
There is actually no need to stop the mailflow before performing the final steps of the migration, just check out the guide posted at
ZxBackup: Incremental migration with ZeXtras Backup - ZeXtras Suite Wiki to see how to perform a downtimeless migration

You'll be able to "update" the data in your STANDBY server while the ACTIVE is still running and then update such data one last time after the mailflow has been switched and the ACTIVE server has been decommissioned.
In your particular case you must change your Mailscanner's transport map during the Step 7 of the guide (when the guide states "Switch the mail flow to the new server").
Stopping Zimbra Desktop clients during the migration will GREATLY improve performances, it's 101% suggested to do so.
A couple of additional hints:
- Data deleted from the ACTIVE server between the final imports will be present on the STANDBY server, as this kind of migration incremental but not differential.
- I don't think that this is the case, but the names you use in your example are dangerously close to those used for failover environments... ZeXtras Suite is not made to allow that kind of operational mode (well, not yet :P)
Keep us up to date with your migration process and feel free to ask any further questions you sould have!
Have a nice day,
Cine
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