Travel on I797 and an H1b Stamp under a different employer

[dhruva_rk]

Dear Immihelp,

I have my H1b visa stamped under employer A and it valid until OCT 2014. The date on 1-94 is the same.

After which I have changed my jobs and have a new I797 under employer B which is valid until May 2013.

Would it be safe to travel outside the US, under the above scenario ??

I have read numerous blogs and forums and seen that the opinion is varied.
If possible, please direct me towards, any official link (DHS, CBP or USCIS).. which states a rule for the travel as mentioned above


Thanks



Dhruva R. Kamra