Once Jill reaches the mushroom grove and is about to jump up towards the apple, hold down [right]. Instead of jumping up as normal, Jill will freeze for a second then jump to the right. You now have control of Jill. Unfortunately you can't leave the grove (and there doesn't seem to be a way to control her earlier) but this does allow you to actually get the apple (and another 12 points) by jumping around the level-ending point just below the apple, instead of the game ending before you get it, as happens when Jill is not under your control.