L1 to H1B transfer, In USA before H1B petition is approved

I am on L1 visa in USA. Before entering USA my H1B was initiated. After entering USA my H1B petition has come through with Consulate for stamping as Chennai

Do I need to get H1B stamping in my passport to start working on H1B in USA?  How can I do Change of Status when I am in USA.  Is going to Mexico for H1B stamping advisable? How long it will take to get change in consulate in petition from Chennai to Mexico.