Can I send a coupon code to a customer only after they leave a review?

Yes, you can enable this option, as well as send a separate notification for the customer to know that they can now use their coupon code. For this, please, navigate to System > Configuration > Smart Review Reminder > Coupon and set “Publish review to activate coupon” to “Yes”:

Magento Smart Review Reminder extension by AmastyMagento Smart Review Reminder extension by Amasty

See more details on Smart Review Reminder page
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