L1 to H1B Fresh

I have in the US on L1b Visa since 2011 Aug, my L1b Visa expired in Apr 2014 but I had an valid I94 till dec 2016. In the meantime my employer filed a “fresh” h1b for me and it got approved. But he says it is a fresh H1b and until I go back to India to get it stamped I am still on L1B I94 and have not started using H1b.

My question is : I am not looking to stay with thie employer now , can another company file for a H1b trasnfer for me using the H1b Petition ?

Yes, but you will still need a H1 stamp to start working on a H1b. Usually CoS petitions from L1 to H1 are not entertained by the USCIS

Ok… so I can transfer my H1B to another company but cannot work for them until I get it stamped? That is weird, if I do not wish to travel outside US to get it stamped, I cannot work?