I have a customer that runs Zimbra, they want to be able to schedule an appointment in Zimbra then have Zimbra push the appointment to Exchange.

The reason is that there is a product that uses Exchange for it's calendaring functionality. We do not want the user to do anything different in their current environment of scheduling.

Is there a way to have Zimbra push the calendar invite to Exchange and for Exchange to interact with Zimbra.

From the customer perspective there is NO outlook or exchange.