Incoming Mail Log does not have to be migrated to Cloud.
On the Server platform, a Purge strategy can also be specified, as log entries are stored locally, but there is no counterpart for this feature in the Cloud app.
Migrate Log Entries not possible
As of now, there is no way to migrate existing log entries from the Server App to the Cloud App.
An automated migration tool will be available later this year which will make it possible.