I’ve done something like this using Zapier.

You can’t retrieve user email from a google review that’s probably why klaviyo is not making this integration.

However with zapier :

• I grab the name of the user that left a review 
• then I look it up on shopify wich allows me to get the email of the person ( if they’re a customer or subscribed to the newsletter only )
• Then I send the email through Gmail ( but you can also add it to any klaviyo flow list or segment and klaviyo will take it from there )

Hope that helps :)