Cacher is the code snippet organizer for pro developers

<?php

/*
 * Documentation
 * https://codex.wordpress.org/Plugin_API/Filter_Reference/send_password_change_email
 * https://codex.wordpress.org/Plugin_API/Filter_Reference/send_email_change_email
 */

// Add below this line to functions.php

// Add this to prevent sending password change notification:
add_filter( 'send_email_change_email', '__return_false' );

// Add this to prevent sending email change notification:
add_filter( 'send_password_change_email', '__return_false' );