SmarterMail provides this in the application:
https://portal.smartertools.com/kb/a2711/import-mailbox-data-to-smartermail-from-third-party-mail-servers.aspx
It works ok. It is a fire and forget type of thing, can't get interrupted during the import, can't delineate duplicate items, etc, etc. For small mailboxes, it works great.
Most of the time we use MigrationWiz. Much, much more feature rich, but you also pay $12/mailbox to move it. But, when moving a large amount of clients over from Exchange to SM or even from IMAP to SM, it works great. One million times better than touching every users Outlook, using powershell to dump PST from Exchange, etc, etc.