Trying to put a box on a moving lift

Hi guys ,
in my level i am having a lift, made with matinee. I want to use it to transfer some boxes on the other side of the obstacle.
And if there is something beneath the lift, while it is moving i want to make it stop. OK , so far so good , i made an invisible
box(not rendered in game) and when the lift reaches it, i am firing a trace to see if there is something beneath it, if there is , stop playing the Matinee.
Then I added a delay of 3 seconds and fired the trace again , if hit again do the same , if NO i have a branch , start playing the Matinee.

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This is doing the trick , stopping and playing the lift, but how about putting the box on it and making it move with the lift?

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I am thinking of "Attach actor to actor " , but I can not think out the logic I should use? If they begin to overlap(the lift and the box), but they can overlap when the lift is over the box , and if I attach to it then ,that wont do the trick, right? I want to attach the box to the lift, only when the lift is in it’s lowest state.

Thanks for any help!