The source forum has a link in the list of threads, which you probably know already. Do you mean in the destination forum? Interesting question.
Have you seen situations where it was confusing what the source forum of a thread was? Like you say, usually if we move a post to a different forum and it might be confusing (especially for homework threads), we try to add a note in the OP to mention that the thread has been moved.
If we move a thread from, say, Quantum Physics to Classical Physics, we would not usually mention anything in the thread (but the OP is notified by default about the thread move).