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The feature of email redirecting is also known as remailing or resending.
The extension is an answer for bug 12916
Not all email providers support redirection of messages. Most notably Microsoft does not support it at the moment, probably as a measure against SPAM. I think they do this in error, and also reported this to Microsoft, but unfortunately they haven't changed their policy yet.
If you run into issues with an email provider not supporting redirection of messages, please contact them and see if you can make them change their policy. You can point them to this add-on, bug 12916, or RFC2822 section 3.6.6.
As a workaround you can also redirect your messages through another email provider, e.g. Gmail, but this isn't always desirable, because then that email provider gains access to the messages you redirect, and those messages might contain sensitive information.