Can we display Joomla Login Module in WordPress?

Hi I am using Joomla and WordPress both and I use a single sign-on plugin which is Joomla based. Now the issue is that it is kind of one-way login management.

What I mean is When a user logs into Joomla he automatically gets logged into WordPress and similarly when a user registers into Joomla his details are automatically replicated into WordPress. This activity does not happen when a user logs into or registers from WordPress.

So I wanted to know Is there a way to display the Joomla Login module in the WordPress pages so that when a user logs in from a WordPress page he gets his credentials checked from the Joomla database and the rest is handled by my Joomla Single-signon plugin.

Or is there a better way around?

Kindly suggest.

The code for my Joomla Login Module is somewhat like this:

<?php
defined('_JEXEC') or die('Restricted access'); ?>
<?php if($type == 'logout') : ?>
<form action="index.php" method="post" name="login" id="form-login">
<?php if ($params->get('greeting')) : ?>
    <div class="user-greeting">
    <?php if ($params->get('name')) : {
        echo JText::sprintf( 'HINAME', $user->get('name') );
    } else : {
        echo JText::sprintf( 'HINAME', $user->get('username') );
    } endif; ?>
    </div>
<?php endif; ?>
    <div class="readon"><input type="submit" name="Submit" class="button" value="<?php echo JText::_( 'BUTTON_LOGOUT'); ?>" /></div>

    <input type="hidden" name="option" value="com_user" />
    <input type="hidden" name="task" value="logout" />
    <input type="hidden" name="return" value="<?php echo $return; ?>" />
</form>
<?php else : ?>
<?php if(JPluginHelper::isEnabled('authentication', 'openid')) :
        $lang->load( 'plg_authentication_openid', JPATH_ADMINISTRATOR );
        $langScript =   'var JLanguage = {};'.
                        ' JLanguage.WHAT_IS_OPENID = ''.JText::_( 'WHAT_IS_OPENID' ).'';'.
                        ' JLanguage.LOGIN_WITH_OPENID = ''.JText::_( 'LOGIN_WITH_OPENID' ).'';'.
                        ' JLanguage.NORMAL_LOGIN = ''.JText::_( 'NORMAL_LOGIN' ).'';'.
                        ' var modlogin = 1;';
        $document = &JFactory::getDocument();
        $document->addScriptDeclaration( $langScript );
        JHTML::_('script', 'openid.js');
endif; ?>
<form action="<?php echo JRoute::_( 'index.php', true, $params->get('usesecure')); ?>" method="post" name="login" id="form-login" >
    <?php echo $params->get('pretext'); ?>
    <fieldset class="input">
    <p id="form-login-username">
        <label for="modlgn_username"><?php echo JText::_('Username') ?></label><br />
        <input id="modlgn_username" type="text" name="username" class="inputbox" alt="username" size="18" />
    </p>
    <p id="form-login-password">
        <label for="modlgn_passwd"><?php echo JText::_('Password') ?></label><br />
        <input id="modlgn_passwd" type="password" name="passwd" class="inputbox" size="18" alt="password" />
    </p>
    <?php if(JPluginHelper::isEnabled('system', 'remember')) : ?>
    <p id="form-login-remember">
        <input type="checkbox" name="remember" class="checkbox" value="yes" alt="<?php echo JText::_('Remember me'); ?>" />
        <label class="remember">
            <?php echo JText::_('Remember me'); ?>
        </label>
    </p>
    <?php endif; ?>
    <div class="readon"><input type="submit" name="Submit" class="button" value="<?php echo JText::_('LOGIN') ?>" /></div>
    </fieldset>
    <ul>
        <li>
            <a href="<?php echo JRoute::_( 'index.php?option=com_user&view=reset' ); ?>">
            <?php echo JText::_('FORGOT_YOUR_PASSWORD'); ?></a>
        </li>
        <li>
            <a href="<?php echo JRoute::_( 'index.php?option=com_user&view=remind' ); ?>">
            <?php echo JText::_('FORGOT_YOUR_USERNAME'); ?></a>
        </li>
        <?php
        $usersConfig = &JComponentHelper::getParams( 'com_users' );
        if ($usersConfig->get('allowUserRegistration')) : ?>
        <li>
            <a href="<?php echo JRoute::_( 'index.php?option=com_user&view=register' ); ?>">
                <?php echo JText::_('REGISTER'); ?></a>
        </li>
        <?php endif; ?>
    </ul>
    <?php echo $params->get('posttext'); ?>

    <input type="hidden" name="option" value="com_user" />
    <input type="hidden" name="task" value="login" />
    <input type="hidden" name="return" value="<?php echo $return; ?>" />
    <?php echo JHTML::_( 'form.token' ); ?>
</form>
<?php endif; ?>