Hi, I am working on L1B visa with Company A. Company B applied h1B for me and its approved.

I will be able to start working on H1b from Oct 1st. My question is since My H1B is approve, so can I still work on my L1b Visa after Oct 1st or I have to shift on H1B. I want to join new company-B after Nov or in Dec only. Please suggest.
Thanks,
Ankit Bansal