Concern on H-1B Stamping

[skH1BQuery]

Hi,

 

I was working for organization A in India and for the same organization I moved to US - thus I have that org's name listed as the "Sponsor" on my Visa which is valid for couple of years. Now, I moved from Org A to Org B in US and planning a trip to India in early 2015. Please let me know if I would need to get the visa stamping?

 

I have the Visa stamping till 2016

I have the I94 valid till 2016

 

But, I am not sure if I can use the above which were stamped from Org A.

 

Clarity on this is required ASAP so that I can get the bookings done accordingly.

[jairichi]

You can travel with existing valid visa and org B's I797.

[skH1BQuery]

Thanks @jairichi..

 

Can you point me to a USCIS link (or any documentation for that matter) which would list this understanding - my current org - B, is pretty new for all immigration related concerns so I need to make sure that HR and the Management understand what we discuss here (to avoid any of their concern). 

 

And if I fly from US -> India,

US -> Canada

US -> Mexico,

 

the thumb rule will remain the same at my port of entry (in US) where I need to show them the Org A's visa and Org B's I797 ?