Inveo

This plugin will fully integrate your WordPress with no compromises into any web application supported by the Theme Provider module.
Demo (PS 1.7): <a href="http://demo.inveostore.com/prestashop17/blog/" rel="nofollow ugc">demo.inveostore.com/prestashop17/blog/</a>
Demo (PS 1.6): <a href="http://demo.inveostore.com/prestashop16/blog/" rel="nofollow ugc">demo.inveostore.com/prestashop16/blog/</a>
Live websites: http://www.inveostore.com/info/featured-websites-6
Currently supported web apps: PrestaShop 1.3/1.4/1.5/1.6/1.7 (excellent eCommerce store)
You need to install Theme Provider <a href="http://www.inveostore.com/wp-theme-providers" title="PrestaShop Theme Provider module" rel="nofollow ugc">PrestaShop Module</a> on your ecommerce website to use this plugin.
Features:
<ul>
<li>Integrates WordPress to PrestaShop with a simple click</li>
<li>Automatically adjusts WordPress CSS selectors (restricts WordPress styles only to the WordPress elements)</li>
<li>100% compatibility with other WordPress plugins</li>
<li>Editing of the WordPress or PrestaShop template files not required</li>
<li>Produces a valid (X)HTML source code</li>
</ul>
Support thread (PrestaShop): <a href="https://www.prestashop.com/forums/topic/432988-module-wordpress-blog-integration-to-prestashop-13141516/?view=getlastpost" rel="nofollow ugc">www.prestashop.com/forums/topic/432988-module-wordpress-blog-integration-to-prestashop-13141516/?view=getlastpost</a>
You may also like our <a href="http://www.wp-accelerator.com/wordpress-woocommerce-accelerator-47?utm_source=webmedia&utm_medium=directory&utm_campaign=Wordpress.org" title="WordPress & WooCommerce Accelerator" rel="nofollow ugc">WordPress & WooCommerce Accelerator</a> plugin and the <a href="http://www.presta-accelerator.com/prestashop-accelerator-46?utm_source=webmedia&utm_medium=directory&utm_campaign=Wordpress.org" title="PrestaShop Accelerator" rel="nofollow ugc">PrestaShop Accelerator</a> module.
<h3>License</h3>
This plugin is free for everyone! It is released under the LGPL, which means you can use it free of charge on your personal or commercial blog. But in order to enjoy the full functionality of this plugin, you need to download the Theme Provider module for the web app you want to integrate your WordPress with.

WP Integration

This plugin will fully integrate your WordPress with no compromises into any web application supported by the Theme Provider module.

curlybracket

This plugin will allow you to automatically rehash the passwords of users you have beforehand imported from a Prestashop database to your WordPress database.
This is useful if you are migrating a website from Prestashop to WordPress.
It allows users to authenticate via their email address, like on a Prestashop installation.
Upon login, the plugin will check the password entered by the user, against the value stored in the database. Using the COOKIE_KEY of the former Prestashop installation, it’ll verify if the password is correct and, only in that case, it’ll rehash the password using WordPress’ default hashing algorithm and insert the new password to the database. Then it’ll try logging in.
In every other case, login will function normally, so if there is an error, it’ll be returned.
In a while, every former Prestashop user you have imported to your WP DB will have their passwords securely rehashed.
First tested successfully with Prestashop 1.3.5 and WordPress 3.6. 
Lately tested successfully with Prestashop 1.5.6.1 and WordPress 3.9.

Prestashop User Compatibility

This plugin will automatically rehash the passwords of users you have beforehand imported from a Prestashop database to your WP database.

WP Integration vs Prestashop User Compatibility