Thunderbird can send mail from multiple identities for a single account. This is useful if you have multiple e-mail addresses that all go to single account.
First enter the Account settings by right clicking on the account in the left panel and pick Settings.
Go to Manage identities....
Here you Add... a new identity.
Enter your information. In this example the outgoing mailserver is smtp.uu.se but it should work fine with the Exchange server at mail.uu.se too (as long as the settings for that server are correct). Save.
Send one mail to each of your two addresses. When replying to them Thunderbird will pick the appropriate identity. Here is when replying to a mail sent to email@example.com.
Here is when replying to a mail sent to the other identity firstname.lastname@example.org.