I didn't even know that you can save an IM.
Someone once showed me how to do it and the reason is kind of funny. Several years ago an employee used an office computer inappropriately, instant messaging along the lines of Foley. The employee didn't close out the IM window so it was discovered, reported it to me and then I had to go to HR and find out how to handle. I was instructed how to save it for disciplinary reasons.
You can save an IM while it is still on your screen. I forget if you have to copy and paste it, or if there's an option, but I've done it for one reason or another. Anyone in the chatroom would have that opportunity. I don't know how it works so far as going to "find" an old IM, do they really exist in cyberspace after everyone clicks out of it, I wonder?