He should be able to travel with a valid visa, proof of H-1B transfer, and evidence he has maintained nonimmigrant status. The new I-94 should be valid until the date indicated on the H-1B transfer and extension or his passport validity date, which ever is shorter. You can read more about H-1B visas at http://myattorneyusa.com/work-visas.
Answered on Jun 15th, 2016 at 4:45 AM