When I did that, the moon started orbiting the Sun (parent's parent). When I tried that for the second time, the moon was placed to the centre of its parent and set all orbital elements' values to 0. I was unable to change the values anymore and since the moon is obviously smaller than its parent, I can't even delete it (I can't select it). But I guess the increased mass of the parent grew by some 0,00001% (maybe less), so that's not such a big deal.