I would verify with support but my guess is you maintain your history if you just move the ad group(s) without making any edits.
That is a good question. Give them a ring and see what they say. 1-866-2Google. Report back! Neil SEOstew
I've had Google tell me before that the history is not lost, however my experience with it always seems to be that some if not all the history is lost and I have to start over. And that's with Google doing the moving for me.
How do you move an Ad Group? I've tried and tried to do this, and even scoured through AdWords' help section and found nothing. I end up having to create a new campaign with a new adgroup, and make a new ad and a bogus keyword, then just move the keywords to that new ad group and delete the bogus keyword. They really should have a workaround for this.