H1B Visa Transfer with old visa in the passport

USA H1B Visa
1

I have recently applied for the extension and got it approved. I have the new I797A with me, but yet to go to India and get it stamped. Still my passport has the old Visa.

Is it ok to transfer to a new employee with out the updated Visa in the passport? Please advise.

2

Yes, it is fine, you can. If the old visa is valid, you can use it as well for re-entering.
Read Do you need New H1B Visa Stamping after Transfer? H4? FAQs - RedBus2US

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