Problem: 

I’ve setup the SMTP extension from Mageplaza and successfully sent and email with AWS SES. I tried resetting a user’s password, but the end user never receives the password reset email. 

Solution: 

The password reset emails use the Customer Support email address. If this is not configured SES will not deliver it. 

Go to Stores –> Configuration –> General –> Store Email Addresses and configure your customer support sender email address that is authorized to send through SES.