Right. My point was, if Mrs. Aruns was going to get points, the ticket would have been sent to her. It was sent to the instructor/driving school, so (I believe) she’s not on the hook for any points.
Ah, with you now. I believe the procedure here is that the registered keeper of the car receives a Notice of Intention to Prosecute, which he has to fill in and return, stating who was driving the car at the time – any fines/points come after the driver of the vehicle is established. I’m assuming that’s the stage Mrs Aruns is at, so far, and that she can expect a fixed penalty notice in the post before long.
If I understand correctly, this is what happened, yes. Mrs Aruns told me the instructor looked for her, so I suppose he got it, and I suppose he wants to use the “guilty with explanation” option, but he also told my wife that she is going to get both points and fine, which, even if it is legal, I found a tad unfair (well, life is unfair, but that doesn’t mean we should passively swallow unfairness).
I had a chat with my dad, who is an instructor in Italy and owns his own driving school, and he agreed with me; he said that in any case it shows this instructor is not 100% reliable, having allowed my wife to excess the speed limit. This is not the same at all as the kids in the back saying “Go faster mum”, my dad said, as an instructor is a professional who is paid to teach legal and correct behaviour, with the means of controlling the car (the double set of pedals) in case my wife didn’t want to slow down. He also added that if it happened to him, he would have swallowed the fine and put it down as one of the costs of his business.
Not that it matters since we are in another country anyway, but at least we know we have his sympathy! 
I do think you have a point there, Lars – as the driver, Mrs Aruns is legally liable for the points and fine, but the instructor surely ought to have some professional responsibility to try to ensure she drives safely and legally while she’s under his instruction. Probably not in any legal sense, I suppose, but even if he didn’t know about the camera, he certainly should have known the speed limit and how fast she was driving. I think that unless she was unlucky enough to go over the limit just as she was passing the camera, leaving him no time to react, she could probably make the case to him (or perhaps his company) that he should have done more to keep her at the proper speed. I don’t think she can avoid the points, but I don’t think it’s out of line to ask the instructor to reimburse the cost of the fine, if he’s fallen down on the job. And he wants to keep her as a client.
Can you contest the ticket in the UK? In the US, its generally acknowledged that if you go through the trouble of showing up to traffic court to contest a ticket, you usually get at least 50% discount on the fine, and with the addition of groveling apologies, a reduction in points. Just don’t make a habit of it!
That said, I also wonder about the instructor. When I was taking driving lessons my instructor always kept an eagle eye on the speedometer and judiciously used the second brake when needed.
For the fixed penalty notice, generally no: it’s not worth it. From personal professional (but old) experience, they often add to the penalty. In the OP’s case, it might just be worth it as she’ll be half-way to being banned. I’m not sure how Mrs Aruns could swing it, though: grovelling and asking that it be converted to purely a fine is probably about the best for which she could hope.
I’m not sure I would do it in her shoes either, it looks like a risk I’d not have her run. I wonder if she has a chance of getting into one of those courses they give you here in some cases for your first offence? Not quite sure of that, that fine’s easy tasty money for a half-starved city council, and being easy on the points takes the edge off the zero-tolerance policy they have against speeding drivers.
Unlikely, given that she’s still a learner.
I was surprised to see the cite above that it was the learner’s responsibility. I thought (obviously wrongly) that the instructor/qualified driver was legally responsible if the driver hadn’t passed their test.
I was just thinking about this the other day, actually, as on my way to work I saw the aftermath of a minor accident at a roundabout involving a driving instructor’s car - it looked like the learner had pulled out onto the roundabout and been hit by another car. (The instructor obviously wasn’t on the ball with the dual controls!)