如果新公司开始申请TRANSFER H1B, 那在原公司是不是应该已经通知辞职了。
-It is irrelevant. You need to provide a resignation letter if you want to resign.
在新公司开始申请TRANSFER 到成功拿到以前,还能在原公司继续上班吗?
-Yes, if you want. You can work for the new employer after your new employer files the transfer (get the receipt) if you want.