1- If contacting the insurance company will put his mother in a difficult situation or cause her harm/difficulty, then he should avoid doing that.
2- If the insurance company knew that he was driving and not his mother, would they have fixed the car or they would not have paid anything?
3- If the company is a public company (government company) then it’s ok he can repent and doesn’t need to do anything now. If it’s a private company, he can do the following:
-Call them and anonymously ask them about this scenario. Ask them if years ago someone did this, what’s your company policy towards that? Do you demand that he pays you back or no? It’s probable they say they don’t demand compensation.
-If they said they would demand compensation in such a case, he can estimate how much it cost to fix the car, and then he can anonymously donate that amount to the insurance company.