This app now appears on Google Play (though doesn't appear to like the UK, but I guess I'll obtain it somehow.)

It is a new incarnation of the VMWare Zimbra for Android fling released in 2011.

It can be used with other collaboration software, but gives extra features for Zimbra users.

For example, saved searches, briefcase documents, tasks.

However, reviewers suggest that CardDav (for contacts) and CalDav (for calendars) are more robust, and that only a single calender can be synced(?)

Here is the blog post about the release: Office of the CTO | Introducing VMware Horizon Mail

Here is the app on Google Play: