I797 H1B Approval question

[sarnath]

My wife previously entered the US on J1. Following the completion of her work, she returned to India and after 1.5 years re-entered the US on a B1/B2. She has now been offered a job and the institute is willing to sponsor her H1.

So her current visa status is B1/B2

She still has about 4 months of her 2-year home country residency requirement to complete.

My question is:

Can her employer file for her H1B? I am not talking about the visa. This is regarding the I797 H1B approval notice

I know that she will not be able to leave the country since she cannot get the H1B visa stamp. But can she start working once she gets the I797 H1B approval notice?

Thanks