Can i transfer my H1-B in India even before my first travel to the USA ?

USA H1B Visa
1

hi,

i am currently working for company X in India. I had applied for H1-B from a american company Y this year, and my application got selected in the lottery, approved and stamped.
Now my company X is asking me, if at all you wanted to go to USA, you could as well gone with us. So they are contemplating options where they can get my H1-B visa transferred so that my company X can become the visa sponsor instead of company Y.

  1. Is this type of a H1-B transfer possible even before I set my foot in the united states ?

  2. approximately how much duration is this process going to take ?

Cheers

Duster