Absolutely not. The previous employer has no role at all and does not even have to know it happened - you could apply for a H1b transfer, get it approved, decide you don't want the new job and continue working for your old employer without them ever knowing you had looked around. Everyone I know has had the transfer completed before giving notice at the old job so that if it somehow is denied (eg new employer does not have a job that qualifies for a H1b), the current employer doesn't have to know you wanted to leave.
