My h1b transfer experience
When i did h1 transfer 2 years ago, my new employer attorney told me that as soon as the new employer receive my h1b transfer receipt, i can start work for my new employer. Actually, as soon as my new company attorney received, I gave my old employer 2 week notice.
Bottom line is: Get the receipt for your h1b transfer from USCIS, gave your employer notice, and start work for your new emplyer