Catch mail from wp_mail

Probably you should use the wp_mail filter ( https://codex.wordpress.org/Plugin_API/Filter_Reference/wp_mail ) or just simply use the wp_mail function ( https://codex.wordpress.org/Function_Reference/wp_mail ) to send the email after a specific action.

Then you can store it like:

$status = wp_mail( $email_address, $subject, 'Your Password: ' . $password . ' - ' . $user_id );

If you have a $status then you can insert the email into a post or custom post type with wp_insert_post()