Rated 4 out of 5 stars

Great idea. I installed it but when I sent a test email to my Thunderbird adress there was nothing in my sent mail folder and no emails were sent to the adresses I set the addon to forward the emails to. Why isn't it working??

This review is for a previous version of the add-on (0.7.8). 

Redirected messages are only saved when you save sent messages for the account with which you redirect. This is also shown as a tooltip in the options dialogue of Mail Redirect.
You can check your account settings under Tools → Account Settings → <account> → Copies & Folders.

Also not all ISP's save redirected messages. Especially Gmail doesn't do this, because the redirected message has the same Message-ID as the original message and Gmail doesn't allow more than one message withe the same Message-ID. If you want to see your redirected or other sent messages with Gmail, you'll have to configure your account to store the sent messages under your Local Folders…

With the information you filed in the review I cannot tell why the redirected message wasn't received at the address you send it to. Please file a ticket on the website or send a mail to the mailing list to get more support on this issue.