I see a response message “Your message was sent successfully” with green border, but I never receive a mail for that.

Recently i face this problem. Contact form display successful message sent. But mail is not recieved. All settings are perfect.

After this i installed one plugin. Easy WP SMTP.  Download here
Configure it with server. Set smtp and port. After this contact form perfectly working. 

You can also testmail also. Here is the setting for testing your settings are right or not.