Is it obligatory for my brother to fast two consecutive months for each soul, given that he was 100% at fault in the accident that led to the death of three people?

If the injured parties were the sole cause of the accident (their error was 100%), and your brother could not avoid it, then there is no liability (daman) or expiation (kaffarah) upon him. This is based on the rule: "That which cannot be avoided incurs no liability." This applies to vehicle drivers: if they could have avoided the accident but failed to do so due to their negligence, then liability and expiation are upon them. If they could not avoid it, then there is no liability and no expiation.