B1 to H1B conversion - H1B visa not stamped in passport

USA H1B Visa
1

Being in USA on B1 visa and having the current employer’s H1B copy (i-797a) form with me (H1B not stamped in Passport) , can I apply for H1B transfer to employer B?

Please advise.

2

Yes you can very well apply for transfer as far as you are in US.

Thanks

Vivek