WordPress Not Sending Mail After Moving Site to a New Server
There could be a couple issues causing WordPress to not send mail however in a server move the most likely is that the previous server was using Sendmail and the new server is using a different mail server like Postfix or vice versa. There also are a couple ways to resolve the issue and I will explain each method below however I recommend installing a WordPress Add-on to resolve the issue versus modifying a core WordPress file that could inadvertently be overwritten in the future.
The two ways which are described in detail to resolve this issue are to either install the WP-Mail-SMTP WordPress plugin or to modify the pluggable.php file located in the /wp-root/wp-includes directory. Each method will change the way that the $phpmailer function sends mail.