Old valid visa is good for travel.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.
If your current H-1B was approved and a new I-94 card was issued you will be fine to stay in the US without issue in accordance with the I-94. However if you travel abroad, you will need a new H-1B stamp to re-enter the US. This can be obtained in India or in a 3rd country if your current immigration lawyer believes your case will be reviewed and not deferred to your home country. Many no issue H-1B stamping interviews are conducted in Canada for example. However each consulate has its own rules on 3rd country national visa stamping and each reserves the right to send you to the US embassy or consulate in your home country.
Talk to your employers immigration attorney to see how things stand.
Representing clients throughout the US and around the world: www.PogueImmigrationLaw.com (513) 549-4420. We cannot provide legal advice or recommendations unless you retain our law firm to represent you. No attorney/client relationship will begin until you sign a representation agreement and make a retainer payment to open a case with us. Any information found here is general in nature and should not be relied upon in individual cases.