The fact that it put a decent dent into a classic Mustang means it must have been one heavy branch since the steel on cars of that era was quite a bit thicker than in cars today. Depending on what the rest of the body looks like, when you have to repair a roof, it means replacing the headliner and probably painting the entire car since matching the paint will be nearly impossible between the roof and the body with no seams to separate them. If your son or any of his friends have any auto-body experience this might be a great opportunity to get the car back in running condition and painted since the repair bill will be based on shop prices. Get quotes for having the work done "right" which hopefully means a full paint job, get paid by the insurance company then use the money to get the car in good shape. If it's a desirable year and doesn't have any or many modifications from the original equipment, he could just keep the money and sell the car as is. Nothing unethical about it at all and perfectly legal.
If he happens to have a 65 to 69 fastback, it's worth a small fortune even in not-so-perfect condition. Restored ones go for upwards of $70,000 here in California.
Glad the neighbor owned up to what happened and hopefully he'll do the right thing. Since his tree trimmer wasn't licensed and the job not permitted, he's on the hook for the damage personally, and his home owners insurance may not conver it because of that.