I have integrated it once as below.
register.php is page where user register to the site.
and forum is a sub folder for phpbb placed at root.
<?
/*======================================
my register.php code goes here
========================================*/
//--- phpbb code start ------
echo '<form method="post" style="display:none;" name="frmfrm" id="frmfrm" action="forum/ucp.php?mode=login">
<label for="username">Username: </label> <input type="text" name="username" id="username" value="'.$_POST['username_login'].'" size="40" />
<label for="password">Password: </label><input type="password" name="password" id="password" value="'.$_POST['password_login'].'" size="40" />
<label for="autologin">Remember Me?: </label><input type="checkbox" name="autologin" id="autologin" />
<input type="hidden" value="Log In" name="login" />
<input type="hidden" name="redirect" value="<strong>../register.php</strong>" />
</form>
<script language="javascript">document.frmfrm.submit();</script>';
?> What above code do, it will goes to phpbb and user entry will be done for forum and it will be backed to page as shown in bold.
Try this and let me know your result.