Sync Gmail for Admins

Sync Gmail for Admins

Hello.  We migrated from gmail to Zoho mail a few years ago, but some users want to be able to use gmail.  I have set up dual delivery in the Zoho Mail Admin console.  This is working fine.  I can't figure out how to sync outgoing emails.  Specifically, if something is sent in Gmail it should appear in the sent folder of Zoho Mail.  It would be nice to sync accounts so that folders and/or tags and deleting emails happen in both accounts.  Is there a way to do this as the admin of both Zoho and Google?  I am specifically looking for an admin solution. ~Thanks!