Anyone said to be in a STATUS while they are legally living in US.
While on a STATUS(for your case, its L1), you have applied to change to another status(by your Employer B). Once this Employer B H1 petition approved, you are legally on H1 status and no longer on L status.
You cant request a status for a per-determined date.
BTW, there is nothing called transfer of a status.
Also, YOU cant do anything to your H/L visas, your employer only can do.
To add, just check with your attorney, if they filed it as Change of Status (COS) or Consular processing. If COS, then you are automatically changed to different status. If not, you can do COS later anytime you want.