Google My Business can sometimes transfer your business reviews when you move, set up a new office, change names or whatever. But that is currently not possible. A Local Search Forum thread contains the local SEO people who say that Google is currently unable to do this.
Rich Owings asked Google for it and the Google My Business team told him: "Due to a technical issue, we are currently unable to transfer the assessments. Our engineers are working on the issue, but they have no estimate of when the issue will be resolved. problem is solved, we will further solve the problem. "
As far as I can tell, it still doesn't work. The problem started sometime in July or earlier and from this week on Google said it still doesn't work. aputtock has posted this update from Google:
Forum discussion on Local Search Forums.