The mother definitely needs to contact the teacher herself. I would not approach it by blaming the other kid though. She needs to tell the teacher that her son is having difficulty getting along with another kid in the class and ask for her advice. It is true that kids will pick on another kid if they can get a reaction out of them.
I had this problem with my older son. Starting in preschool, he always seemed to have one kid in each class that pestered him. My son was not shy, but he was the type that other kids could get a reaction out of. I tried to teach my son not to react, but he was just too young to get it. I felt like in several of the cases, the other kid just wanted to be my son's friend and was not sure how to get his attention appropriately. So, I invited the other kid over to our house for a play date. They did not become friends really, but it seemed to help the situation from just one play date that I could supervise. This may be an option if you do not get any help from the teacher.
I had the biggest problem with this in Kindergarten also. It was a little girl that was picking on my son! Unfortunately, the teacher always saw my son's reaction and not the little girl's taunting, so my son was the one that got in trouble. I spoke with several other parents in the class and they all said that no one liked this little girl, she was really annoying. I tried calling the parents, but they were not receptive to working with me on the problem and they ended up contacting the principal to complain about my son. Fortunately, the little girl moved away over the summer and that was the end of that problem.
If the mother does not let the teacher know what is going on, it will likely escalate and her son may end up being blamed for his reactions.
I don't know why exactly, but my son never seemed to have a problem with this after Kindergarten. I spent a lot of time talking with him about controlling his reactions and even practiced role playing with him.