His mother is the owner and not a UK resident.
That makes no difference. The law is
on this page and there's a view on it in this quotation on this exact subject:
Chief Constable Suzette Davenport, national lead for roads policing said:
Regardless of their country of origin, or that of their car, it is the responsibility of every driver to ensure that they are obeying the laws that govern our roads in the UK, and that includes falling in line with the laws on taxation, registration and insurance as well as those on safe driving."
Note the words, "or that of their car", for which read motor vehicle of course. His motorbike has to registered here, taxed and also insured under it's UK registration. Without that he might be riding without insurance.
I think this is what he might be relying on:
You may be able to use a vehicle with non-UK number plates for longer than a 6-month period, without taxing or registering it, if all the following apply:
- you’re a student or worker
- you normally live outside the EU
- you’re in the UK for a set study or work period
- the vehicle is registered in its home country
Clearly neither he nor the owner don't normally live outside the EU.
.