Xiaobaitum Pjang, or other experts: Question regarding H-1B tran

To all the experts, I have some questions regarding H-1B transfer. Currently I am working for Company A and I accepted an offer from Company B. I plan to do the H-1B transfer.

1) Can I start working for Company B anytime after the H-1B transfer is filed and the receipt is received?

2) Can I still legally work for Company A (before my last day, have not told company A yet) after the H-1B transfer is filed and before it is approved? For example, if I plan my last day the early July, can I still legally work for Company A until July while the H-1B transfer is filed in June (assume the transfer will not be approved before my last day)?

Thank you in advance.