Yes, but I'd advise you to make sure that both computers are set to use IMAP. I don't think it's helpful to think of email being "sent to" a computer. Email sent to you is accepted on your behalf by a server, which is operated by your email provider, very often your ISP. An email client, such as Thunderbird, is a program that you run on your computer and it connects to that server and asks it for any messages that have arrived. In principle you could have any number of separate computers or phones or tablets all asking that same server for email messages. There are two systems that can be used. With POP, the email client asks the server for the messages, and they are given to the client and erased from the server. So you only get one copy and it is stored on whichever computer asked first. With IMAP the messages remain on the server and the computer is given its own copy. You could use POP. I presume you would switch off the home computer and the travelling computer will collect and send your messages instead. But after your trip you'll have some correspondence on the portable computer that you took with you and no easy way to copy it back to your main computer. If you use IMAP then all the messages, including those you sent, or those you filed into different folders while travelling remain available to both computers. To check what you are currently using, open Account Settings and look at Server Settings. Right at the top of the server settings page it tells you the server type.