You've given lots of details, but it's not the details we need, unfortunately.
Firstly, the circumstances when it failed. Was she riding the bike? If so, was she going uphill, downhill? Did she stop at traffic lights, then it wouldn't go or what?
Can I make a suggestion about the Cambridge shop? What about ringing them and asking them what they found, how and why they came to the conclusion they did? maybe they did a specific test and found a specific fault, but that would be very unusual. Most would check the battery voltage and if it was OK but the bike not working, they'd blame the controller. We need to be sure, otherwise you'll spend money and go to a lot of trouble to solve a problem that doesn't exist, leaving your with the real problem unsolved and a bike that still doesn't work.
We know that all this is new to you and it seems confusing because it's like Chinese writing, but it really is simple and we can guide you through how to find the problem and fix it.
Thanks for the pictures, but you sent 2 we already had and the other two show the same thing. none of them show the connectors. Follow the wires until you come to a connector, unplug each and show what pins they have if they're the moulded type, otherwise if they're the block type, show the wires as well.
There should be a motor connector on the left front fork. Wiggle it apart, count the pins ( normally 3 or 9) and push it back in all the way until the edge of the outer part meets the marked line on the inner one. don't just push it in until you think it's tight.