By default, Classic Migration Mode within the Metalogix Essentials application will retain core authorship properties (Created/Modified By and Created/Modified At). However, when migrating lists that require Content Approval, it is possible to preserve the current approval status. In such lists, under "List Copy Options", there is a section for Authorship. Using the remote SharePoint API, the application can currently only preserve either the core authorship properties or the approval status, but not both.
NOTE: Preserving Approval is not supported in Hyper Migration Mode.