This takes advantage of new features in Amazon's Marketplace API (MAPI).
Review Request is offered by Amazon as an option within each order in Seller Central. You can go into any order in Seller Central and click the button:
Amazon then sends the review request to the customer. Convenient, but very manually intensive.
SellerMail allows you to automate this function.
With the MAPI enabled (see Settings > Seller Accounts in your ManageByStats for steps to authorize, if you haven't already), a new Type option appears when creating an Email Rule:
Select this and your email rule becomes an automatic trigger for Amazon's Review Request feature.
Note: follow the steps in the Email Rules section of this Knowledge Base to set up the rest of the rule, taking the following into consideration.
First, there's a time window in which the Review Request can be used. Make sure you set your delay (Send this email __ days) to fall within that window.
Recommended best practice is 7 to 9 days, though anything in that window works. Just be aware Amazon will strictly adhere to that span of days.
Second, unlike other Email Rules, there is no message composition body for this. Amazon sends a standard email, we're just triggering it based on the criteria you set.
Here's a sample of what the Amazon email can look like, and what the customer sees: