What if Your Ball Lands on Another Hole's Green?

Well, it can happen. An inaccurate shot from off the tee, or perhaps fairway, could send the ball onto the green of an adjacent hole. If a ball lands on the wrong putting green the R&A book states that:

"On the Putting Green: If the ball lies on the putting green, the
player must lift the ball and place it, without penalty, at the nearest
point of relief that is not in a hazard or, if complete relief is
impossible, at the nearest position to where it lay that affords
maximum available relief from the condition, but not nearer the
hole and not in a hazard. The nearest point of relief or maximum
available relief may be off the putting green."

 As such, you should certainly not play the ball as it lies. Yet you don't have to retake the shot from the tee or fairway either, and instead get a free drop near to the green.