H1B Extension approved and filling a new amendment

[Raj Tarun 123]

Hi Everyone,

My H1B Extension has been approved recently under premium processing which was filed by my employer with client "A" (where I work now) and it still haven't kicked in yet.

My I-94 expires at the end of august and with this new three year extension approval, I was hoping that it will kick in soon and get extended for 3 more years.

But, I got an opportunity to move to a new client B on a new contract assignment. Now, I have to apply for amendment before my extension kicks in.

How does this work? Is it valid to just apply amendment with the new client "B" or should my employer apply for Extension + Amendment all over again with client B info?  Client "B" is hoping that I could join soon in 2 weeks or so. 

Please suggest.

Thanks in advance.