Hi.
I also had this problem, but just give it time. Eventually it works, but it took 11 hours!
Originally I was trying to also copy photos etc, but gave up.
When I selected just google account and text messages but not photos it was about 1.2GB.
The phone (iphone6s) looked like it was stuck at 'moving items into place', but eventually, after about 10 or 11 hours it said 'complete'.
So....it would be really good if apple could advise on the iphone (or on the android app) that this process may take a long time (12-24 hours). Because lots of people think it is stuck, but it is actually really slow.
I could tell that something was happening because the phone was using quite a lot of battery during this time.
I would advise leaving your iphone connected to a charger while you are doing this, otherwise it might go flat after about 12-14 hours.
Bottom line....STICK WITH IT. Wait it out. Be patient.