You ask a colleague for a file and later find it yourself. They may still spend time searching unless you tell them the request is closed.
Send a short update through the same channel. Say that you have what you need and thank them for considering the request. If they have already begun work, acknowledge that and check whether anything useful should still be handed over.
Close changed arrangements too
When a plan is cancelled or a task changes, tell people whose contribution is no longer required. Remove obsolete reminders where they might lead someone to continue unnecessary work. Protect any private material they sent according to the relevant requirements.
Keep the update proportionate to the request. A minor question may need only one sentence; a changed project may need a clear decision note. Closing the loop gives the other person usable information about their time and attention. It also leaves a cleaner record when someone later checks which requests are still waiting for an answer.
