Rated 5 out of 5 stars

It's a very good plugin that does work but only with correct settings. Here is the step by step tutorial on how to configure TZPush for Outlook.com:
http://www.itechtics.com/how-to-synchronize-outlook-com-contacts-with-thunderbird-addressbook/

This review is for a previous version of the add-on (1.9.8.6).