By default, you and your customers will have to login using your username. This is not practicall since WooCommerce will auto-generate usernames for your customers and they will often forget what their username is. This plugin will resolve that by enabling your users to login using their e-mail address.
<ul>
<li>Works with WooCommerce</li>
<li>Perfect with Klarna Checkout</li>
</ul>

WooCommerce E-mail Login

Enables you and your customers to login with your e-mail address as well as your username.

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.

WooCommerce E-mail Login vs Prestashop User Compatibility