"Can he continue to work for his original company 'A'?"
答案是YES,但没有说的是你必须重新申请TRANSFER,因为你是用的同一个名额.如果你是分别用的两个名额当然不用担心.
"A person can have multiple H1, but can work for only one company at a time" 是错误的.一个人可以同时有两个H-1,一个为A公司FULL TIME工作,一个为B公司PART TIME工作.