You understand that Thunderbird needs to be running for this filtering and forwarding to take place? If you are sitting there in front of it, you can see all the messages anyway, so what is achieved by forwarding them? If you're not sitting in front of it, do you really want to leave it up and running 24/7? Better to do such re-direction at the respective email accounts' websites. Then the messages will seamlessly appear in the target account's Inbox. Forwarding by an email client is quite destructive, since all the transferred messages will say that they were sent by you, losing their context and provenance. Within Thunderbird, it could be a simple matter of moving/copying to a different folder, so there's no need to "forward" as such. If IMAP is being used, the messages will appear in the destination accounts' folders.