B1 - H1B transfer

Dear Experts

I have both B1/B2 and H1B . These two visa were processed by my previous employer and I traveled with the both the VISA in different times.

So, I got my SSN also.

Now I have a doubt. My present company asking me to travel to with a B1/B2 visa.

If I travel with B1 and H1 is not cancelled, can I initiate transfer of my H1B within US if any US employer would like to transfer it?

Thanks for your answer in advance!!!