I'm in L1-B status with H1 approved, can I change employer?

[dbar]

I'm currently working for Company A in L1-B status. Company A filed both a L1-B renewal petition and a new H1-B petition for me as my L1-B approached expiration. Both the L1-B and the H1-B got approved recently. I remain in L1-B status.

Now Company B is interested in hiring me. Can Company B file for a H1-B transfer of my recently approved H1-B even though I'm still on the L1-B?