An email was sent to me in the wrong conversation history.
Hence I would like to move that email from the wrong folder to the right one (and to the right conversation).
When I right-click the email and select “move to folder”, the whole conversation gets moved.
How to have one email only moved?
So, as you have discovered there is a difference between a message and a conversation. When conversations are enabled, the message list is actually a conversation list. Right-clicking on one in the list is selecting the conversation, not the message.
To move a message, right-click on it in the message preview section.
Conversations are determined by details in the message header, so no matter which folder you move it to, it will still be displayed in the same conversation. That is why you have sent messages displayed along with received messages in the Inbox. They are in different folders, but they are the same conversation.
You can disable conversations in Menu > View > Conversations if that works better for you.
Thanks for the lightning-fast reply.
I checked all three display possibilities in the view section, and I will keep to “Show conversations in all views” as I still find it more readable.
I guess I should then just vary my subject lines to avoid confusion from the colleague 
It is not just the subject that is taken into account when grouping a conversation, but yes, sometimes it is useful to vary the subject. 