I can't see how the woman could take out a comprehensive insurance policy as she has no 'insurable interest' in the vehicle itself. (It would be akin to me seeking to insure someone else's house, with me as the beneficiary of the policy if it was damaged in a storm. I can't do so because I have no 'insurable interest').
However a third-party-only policy isn't actually insuring the vehicle itself. It's the driver who becomes insured against having to pay out for injury or damage if they cause an accident. The woman does have such an insurable interest and so there's nothing barring her (in principle) from taking out a policy.
However:
(a) I doubt that she'd find an insurer willing to provide such cover ; and
(b) the owner of a vehicle (and/or their agent) is entitled to say who can, and who can't, drive it. So, irrespective of any insurance issues, I can't see how she can expect to drive the car.