Advanced settings of mailing lists and Mailman archives are not transferred by Plesk Migrator.
Migration & Transfer Manager transfers only basic settings of mailing lists: list administrator, subscribers. Mailing list archives and other settings are not transferred, since Plesk cannot manage them.
It is possible to transfer configuration of mailing list(s) using Mailman's
If you want Plesk Migrator to transfer Mailman archives, vote for this functionality on Plesk UserVoice.