If both computers are set for IMAP access.

Hi David

I checked an both were set to IMAP

Am i right in thinking that they should delete or archive from both?

That's tricky, as Thunderbird offers options on how to process deletes and archives. One might specify delete immediately, while the other moves it to trash. You need to carefully review each for such differences.

I am not fussed it the message deletes or archives. The problem i have at the minute is, if my colleague reads and responds to a message on her pc, it shows as not being read on mine, so it gets confusing as we have to keep checking with each other that something has been read.

Well, there is a timing issue. IMAP was intended for a single person initially, and use by multiple users has its challenges. For example, of the other person reads the message first, the server marks it read. Then, if you open that account later, the message appears read. BUT, if you both access the server prior to either of you reading it, Thunderbird brings in the unread copy. Now, it shows as unread for both of you. When one of you reads it, the status of unread remains for the other. So, you need a plan. One possibility would be to use a tag you both agree to and set that when a message has been read. Test it first, as some servers don't monitor tags. Another possibility is to set up a folder for read messages and drag it there after reading it.