Can you get a copy of your mother-in-law’s driving licence and passport and her ticket whereby she came to the UK and returned?
Anyone who stopped for speeding could simply say that it was there mother-in-law in Australia or Italy or whatever and hence, if you are going to say that it was your mother-in-law that was driving the car, you will need to prove that she exists, that she drives, and that she was here at the time of the offence. Hence, you will need the ticket.
If you have all that information, it’s likely that it will simply be dropped because they will not apply to have her extradited back to the UK for the offence.
What you need to do is fill the section 172 notice in, giving your mother-in-law’s details and giving the information which I suggested and in particular, most importantly, the travel ticket.
Can I clarify anything else for you?
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We can still exchange emails. Best wishes. FES.