H1-B approved but still on L1-B, 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 H1-B petition earlier this year. Both the L1-B and the H1-B got approved, though I'm currently still in L1-B status.

Now a different employer, Company B, may offer me a new job. Since I have the H1-B I-797 Approval Notice, can Company B file a H1-B Transfer directly even though I'm still on the L1-B status and haven't activated the H1-B status yet?