Move them to the Local Folders account. The safest way is first to create new folders under that account (right click on Local Folders and select 'new folder'), then copy-and-paste the messages from their existing folders to the new ones. You can just drag-and-drop messages, indeed whole folders, but I've known things go astray when I've done that. Bear in mind that once the messages are in Local Folders they aren't on a server somewhere else. So if you want to keep them safe you need to keep a regular backup copy of your Thunderbird profile -- that's good practice anyway.

amanchesterman said

Move them to the Local Folders account.

A friend had everything in Local Folders, but they still all got deleted when the old email account was deleted. I currently have 2 accounts, the old one that no longer works and the new one. I have a lot of Local Folders which contain a mix of the emails from the 2 accounts. I am wondering if, to remove the old account, it would be safer to enter the new account information into the old account rather than delete the old account. I have PC Windows 10 and Thunderbird 45.2.0 (up to date)