First, I am sorry to hear of your brother's accident and wish him the fullest recovery possible.
 
Does your brother have access to an occupational therapist?
 
There are specific techniques occupational therapists use to help those who are right-hand dominant learn to use their left hands for writing if necessary.
 
This is absolutely possible although it is not as simple as just practicing with the left hand.  Handedness is controlled by brain activity and so your brain needs to relearn certain skills when it becomes necessary to switch hands.
 
If your brother cannot attend therapy sessions, you may wish to check out the book "Handwriting for Heroes," which describes how to learn to use the non-dominant hand to write.  I have not used the book myself but you may find it helpful.
 
You may also find more information at the Handedness Institute, including exercises for promoting ambidexterity:
http://handedness.org/
 
Your brother may also want to look into additional support while he is re-learning how to write.  There may be programs available through his school or other organizations that can help him obtain a laptop for typing notes and papers, a device to record classes or lectures, and/or an aide or other student to help ensure his notes are thorough.
 
Again, I wish the best for your brother and hope he has great success in his studies.
 
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Candace Lindemann, Ed.M. - JustAsk Expert
Educational Consultant
http://CandaceLindemann.com