Here's how to make your IMAP account inbox available offline in Mozilla Thunderbird, so you can read and write emails offline. The instructions were tested on version 78 (the most recent version is from June 2021), but should apply to earlier versions as well.

This method will automatically download all messages to your computer.

Select Tools > Account Settings from the menu.

Select the Sync & Storage category for the desired IMAP account. Select Keep messages for this account on this computer.