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The plugin replaces your comment form and includes one that also allows to use the facebook credentials.
Special Features:
<ul>
<li>When users comments on your blog they can choose to send notifications to their Facebook Wall.</li>
<li>Notification is automatically sent to the facebook application wall when a comment is submitted.</li>
<li>Simple Facebook Integration.</li>
<li>Using the plugin should increase the traffic and visibility of your blog.</li>
<li>More easy to comment.</li>
</ul>
Visit the <a href="http://web-argument.com/wordpress-comments-switcher/" rel="nofollow ugc">Plugin Page</a> to see the plugin working.

Comments Switcher

Allows users to comment on your blog using the facebook credentials or the default wordpress guest credentials.

Heateor Support

Fancy Facebook Comments enables your website visitors to leave comments using their Facebook account without the need to create account at your website.
This plugin makes it very easy to integrate Facebook Comments with your WordPress website. After just installing and activating the plugin, Facebook Comments get integrated at the webpages of your website with default configuration.
This plugin is also helpful to get traffic to your website from Facebook. Other than that, Facebook Comments is one of the best ways to Socially Optimize your website.
If takes just 5 seconds to integrate Facebook Comments at your website using this plugin: 
1. Download the plugin from this page (1.5 seconds) 
2. Navigate to Plugins > Add New page from left sidebar in admin panel of your website. Click Upload Plugin, click Choose file, upload the plugin zip and click Install Now button (2.5 seconds) 
3. Activate the plugin (1 second)
<h4>Key Features</h4>
<ul>
<li><a href="http://support.heateor.com/gdpr-and-our-plugins" rel="nofollow ugc">GDPR Compliant</a></li>
<li>Recover comments lost after installing SSL</li>
<li>Compatible with Gutenberg editor</li>
<li>Compatible with PHP 8</li>
<li>Can be upgraded to <a href="https://www.heateor.com/fancy-facebook-comments-pro" rel="nofollow ugc">Pro version</a></li>
<li>Post comment on Facebook timeline along with posting at the webpage</li>
<li>Website visitors can sort comments by Time or Social Ranking in real-time using the menu on the top right of the Facebook Comments interface</li>
<li>Set default comment ordering from plugin options page</li>
<li>Change language of Facebook Comments</li>
<li>Enable/Disable Facebook Comments on default posts, pages</li>
<li>Enable/Disable Facebook Comments on custom posts</li>
<li>Enable/Disable Facebook Comments on WooCommerce products</li>
<li>Enable/Disable Facebook Comments on BuddyPress activities and groups</li>
<li>Enable/Disable Facebook Comments on BBPress topics and forums</li>
<li>Free options to customize the look and design of Facebook Comments interface </li>
<li>Mobile Responsive</li>
<li>Widget and Shortcode</li>
<li>Compatible with BuddyPress, BBPress, WooCommerce</li>
<li>Multisite Compatible</li>
<li>Supports HTTPS enabled websites</li>
<li>24/7 quickest support</li>
</ul>
<h4>What makes this plugin Stand Out from others?</h4>
<ol>
<li>Free: Yea, right. It is a free plugin. You need not pay single penny to use the features of this plugin.</li>
<li>No Need to Register Anywhere: You do not need to create account at our website to use this plugin.</li>
<li>No Middle Layer: Plugin runs totally on your website server without any communication to our servers.</li>
<li>Absolutely Simple: Plugin configuration is kept dead simple. Screenshots are provided with options wherever required.</li>
<li>Free Customization Options: There are options available to customize the look of Facebook Comments interface within the plugin, for FREE.</li>
<li>Mobile Responsive: Facebook Comments interface adjusts itself automatically according to the width of device.</li>
<li>Lightweight Code: Our developers follow best coding practices to ensure efficient loading and performance.</li>
<li>We promise to provide best quality among other similar plugins. If you find our plugin is lacking some feature, you can email us and we will do our best to include that feature in our plugin as soon as possible.</li>
<li>Our support team is working 24/7 to answer your queries and assist you. You will find us the quickest to respond.</li>
</ol>
<h4>Important links</h4>
<ul>
<li><a href="https://www.heateor.com/fancy-facebook-comments/#live_demo" rel="nofollow ugc">Live Demo</a></li>
<li><a href="https://www.heateor.com/fancy-facebook-comments-pro" rel="nofollow ugc">Upgrade to Pro version</a></li>
<li><a href="https://www.heateor.com" rel="nofollow ugc">About Us</a></li>
<li><a href="https://www.facebook.com/Heateor" rel="nofollow ugc">Our Facebook Page</a></li>
<li><a href="https://plus.google.com/+Heateor" rel="nofollow ugc">Our GooglePlus Page</a></li>
<li><a href="https://twitter.com/Heateor" rel="nofollow ugc">Our Twitter Page</a></li>
<li><a href="http://support.heateor.com" rel="nofollow ugc">Support Documentation</a></li>
<li><a href="https://www.heateor.com/add-ons" rel="nofollow ugc">Add-Ons</a></li>
</ul>
You can provide your feedback at hello[at]heateor[dot]com

Fancy Comments WordPress

This plugin is what I wanted! I just install it and it works!!

Very easy to use

Integrate Facebook Comments with your WordPress website easiest possible way

Comments Switcher vs Fancy Comments WordPress