When do you think they switched the real Amy for the flesh Amy??

She was on the run on Earth by herself for months so it was pretty easy to take her.
They just needed to take her while she was asleep or put a sleeping pill in her food. Then they just had to create a ganger and hook her up to the machine. The ganger would wake up and because Amy has no idea what happened or what a ganger is she wouldn't see any difference.