L1B to H1b COS (Cap Exempted) - When can I start working for H1 employer

[i_like_usa]

My Situation:

I'm on L1B visa currently in US, my new employer has new petition for new H1b (Change of Status NOT CP) thru cap exempt category (using old/unused H1b in last 6 years) thru Premium Processing.
I expect this new H1b petition will be approved in next 15 days. I have not submitted my resignation for my L1b position to avoid the risk of resigning before H1 Approval.

My plan is to resign and serve the notice period upon H1b Approval. After serving notice period, I'll join new H1b position.

My Question

Can I continue work on L1B visa for few more weeks to serve notice period once after my H1 is approved? Is it legal?

If it is illegal for me to work a single day on L1b position after H1 approval, what are my options/workaround to properly server two weeks of notice period to my current employer and move on to H1b employer?

Thanks in advance for your response to my query

[raghvi]

My Situation:

I'm on L1B visa currently in US, my new employer has new petition for new H1b (Change of Status NOT CP) thru cap exempt category (using old/unused H1b in last 6 years) thru Premium Processing.
I expect this new H1b petition will be approved in next 15 days. I have not submitted my resignation for my L1b position to avoid the risk of resigning before H1 Approval.

My plan is to resign and serve the notice period upon H1b Approval. After serving notice period, I'll join new H1b position.

My Question

Can I continue work on L1B visa for few more weeks to serve notice period once after my H1 is approved? Is it legal?

If it is illegal for me to work a single day on L1b position after H1 approval, what are my options/workaround to properly server two weeks of notice period to my current employer and move on to H1b employer?

Thanks in advance for your response to my query

The future employer can put a specific date of COS in order to accommodate the notice period. It is not legal to work for L1 employer after COS to H1 date.

This is my opinion not legal advice.