Out of interest is there any reason behind why you lose the history as it seems pointless to move the advert. I presume as in my case the main reason of wanting to move an adgroup is to dedicate a budget to the adgroup and aim on improving the adgroup.
At the moment the adgroup is performing well in the campaign however if I move it I am only going to suffer in spiraling costs when all I want to do is allow more money to be spent