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 Magento database to your WordPress database.
This is useful if you are migrating a website from Magento to WordPress.
It allows users to authenticate via their email address, like on a Magento installation.
Upon login, the plugin will check the password entered by the user, against the value stored in the database. 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 Magento user you have imported to your WP DB will have their passwords securely rehashed.
Tested successfully with Magento 1.8.0.0 and WordPress 3.7.1.

Magento User Compatibility

It Works

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

WooCommerce E-mail Login vs Magento User Compatibility