At least your friend should be prove that he/she owns the vehicle from the finance payments � but if a friend of mine told me this story, I would immediately be suspicious that he/she was in league with the garage, not insuring the vehicle in his/her name.
To tax the vehicle, the garage would have had to take your friends money and insurance documents. What kindly garage would take the time & trouble to do this for nothing? Your friends insurance company would want to know whether he/she was the registered owner of the vehicle � which seems in doubt.
I suspect the garage were claiming insurance under their policy, and that is why your friend was going along with this.
Your friend has now discovered the problems with such an arrangement.