Migrating Content from Zimbra or another Google Account
Once you've gone through the Quick Start, look here for more detailed information about moving your Contacts, Calendars, and Briefcase files to Google Apps.
Contact Support

  Migrate your Contacts to GMail

  Migrate your Calendars to Google Calendar
Copy your contacts and calendars from your Zimbra account to GMail and Google Calendar
  Migrate your Zimbra Briefcase to Google Drive
Copy files and folders from your Zimbra Briefcase to Google Drive. We strongly recommend that you familiarize yourself with Google Drive before attempting to copy your briefcase. Click on the Docs and Drive link to the left for further information.
  Copy calendars from another Google account
Copying calendars between Google accounts is relatively easy.