L1 to H1 change of status - urgent

[pnpnpn]

I am currently working for company A on L1
Company B processed my H1 and the approval has come through.
I am not in the payrolls of company B.
I plan to quit company A next week. Am I out of status ?
I will be getting a paystub from company A after the H1 approval came through.
Is this okay ?
If not what are my options ?

[H1Bcap]

should be fine

Once your H1B is approved, the approval date is the formal milestone of status change from L1 to H1. Usually, this kind of notice comes with a I-94 attachment indicating this change. In that case, no matter what you do, you are on H1B, no more L1. If not, be careful what you do, you have to go through CP get your H1B visa stamped. Make sure your notice has the I-94 form.

There is no law to forbit an alien having two H1B(s) jobs. But L1 and H1 at same time, I believe it's not allowed.