I use conversation mode and usually move my sent messages to reception box.
When a new message arrives, the whole conversation moves up in reception box list.
When an answer is move as described, the conversation remains deep in the list.
Could you check if only received messages are used to place the conversation in the list or if all messages (including sent ones) are used?
I would prefer to get the updated conversation at top of the list, instead onf 1 or two days below.
From my observations it appears that only received messages affect the order of the conversation. Sent messages have no affect.
If you propose this as an idea that both received and sent affect the position, you will have my vote as it is something I would like to see.