I recently consulted for a company that wanted to do an integration between FreePBX and Zendesk.
Call Flow:
When a call comes into the IVR and the caller "presses 2 for support" a support ticket is automagically generated in their Zendesk dashboard.
Using the built in features of the Asterisk AGI (Asterisk Gateway Interface) and the Zendesk API makes this a pretty straightforward task to accomplish.
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