If your started working for your new company on April 21, then you are no longer working for the old company for whom your initial H-1B visa was under and that visa is no longer valid. Once you receive approval on your H-1B transfer then you can obtain a new visa through your H-1B for the new company and return to the US on that visa. Consult with your new company's immigration attorney for more details.
This answer is for informational purposes and does not take the place of a consultation with an experienced immigration attorney. This answer does not create an attorney-client relationship.
It is not possible to travel abroad & reenter on the old H1B visa two months after you have stopped working for the old H1B employer. Not without an H1B approval notice for the new employer.
This is general information only. It is not intended as a substitute for legal advice, and does not create an attorney-client relationship. For legal advice specific to your circumstances, you must consult an attorney in a confidential setting, not in an online forum.
No, that would not be a wise move at all on your part, considering you are no longer working for the original employer through whom you got your H-1B visa and your current EMPLOYER'S petition has not yet been approved. If you insist I suggest you talk to your employer about "elevating" its current pending petition to Premium Processing.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
Talk to the new company's lawyer about premium processing.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Premium Processing is a great way to for your case to be expedited. If your attorney emails premium processing and presents evidence of your family emergency, Premium Processing has the discretion to expedite your case even faster than the 15 days.