This change exploits phpBB’s hook system which allows us to execute custom code in certain phpBB functions/methods without modifying any files. To do this we need to create a new file in our phpBB installation in the includes/hooks/ directory, the file name must begin with hook_ and end with your PHP extension (usually .php.)

includes/hooks/hook_trusted-users.php:

<?php

/**
 * This program is free software. It comes without any warranty, to
 * the extent permitted by applicable law. You can redistribute it
 * and/or modify it under the terms of the Do What The Fuck You Want
 * To Public License, Version 2, as published by Sam Hocevar. See
 * http://sam.zoy.org/wtfpl/COPYING for more details.
 */

if (!defined('IN_PHPBB'))
{
	exit;
}

/**
 * This hook disables the post queue for accounts registered with a trusted
 * e-mail address.
 */
function hook_trusted_users(&$hook)
{
	global $config, $user;

	/**
	 * Skip when the queue is disabled, or this is an administration
	 * session so we don't break the ACP, chances are that administrators
	 * have moderation permissions or more posts than required to post any way.
	 */
	if ($config['enable_queue_trigger'] && !$user->data['session_admin'] && preg_match('#@example\.com$#i', $user->data['user_email']))
	{
		$config['enable_queue_trigger'] = 0; // Disable the post queue for our trusted users
	}
}

$phpbb_hook->register('phpbb_user_session_handler', 'hook_trusted_users');

Once you have dropped the file in place you will need to purge your cache, or just manually delete cache/data_hooks.php.