H1B transfer process

Hi,

I am working with company A in india. Company A got my h1b stamped in oct but never travelled to US. Now I have an offer from one staffing firm in US.
How should the transfer process be. Staffing firm tells me to travel to us with the current stamping itself and produce their offer letter at poe along with the client letter they will give.
Actual transfer of petition will be done after I travel to us.
Is this the right or legal process??
I am a little confused. Please help

There are chances of running into issue at POE, as H1 is a company’s property and you can’t use it for other company. Ask your new employer to file cap-exemption and get H1 approved, then go for stamping. This is a safe process

Is this the only process? As my new employer tells me since my current stamping is valid until 2017 I could travel on existing stamping itself and after my arrival in US they would get a new petition approved. Please suggest.

The process I said is the best bet. As I said, you may run into issues at POE… Be risk free