Q: Why won't Thunderbird save my "Sent" mail?

Answer

By default most IMAP clients will use the "Sent" folder to save sent email. Microsoft however uses the convention "Sent Items". To save yourself some confusion and heartache later, you should set Thunderbird to respect this convention.

1. Go to Edit > Account Settings, then go to Copies & Folders under your MIT email account.
   
   
2. Under When sending messages, automatically: select the Other radio button, then in the drop down navigate to the Sent Items folder for your MIT email (note: not a local folder.)
   
   

For more info see Configure Thunderbird for use with MIT Microsoft 365 Mailboxes