do it online www.personalisedvehicleregistration.service.gov.uk...p

Whilst the car will usually be reallocated it's original registration or a replacement by the sounds of things he won't actually be able/need to put physical plates on it & I doubt that DVLA would care (unless someone repairs it & puts it back on the road).

I assume (possibly incorrectly) that the car remains the property of the original owner until the insurance position is agreed. That being the case he can do what he wants with the registration.