The I-94 and not the visa governs how long you can stay in the U.S. If you left before the I-94 card expired then you have not accumulated any unlawful prsence that woudl affect future entries. That being said each time you enter the CBP Officer can judge your nonimmigrant intent based on what you say, your current visa and how much time you have spent in the U.s. recently.
Lynne R. Feldman, Attorney at Law
Concentrating in Immigration Law
2221 Camino Del Rio South, Suite 201
San Diego, CA 92108 | (619) 299-9600
Fax: (619) 923-3277
Former Adjunct Professor -- Immigration law
University of Illinois College of Law
Need additional facts to be answer this question, i would recommend that you consult with an immigration attorney prior to deciding to travel on B1/B2, which was issued prior to issuance of L1-B. It appears your B1/B2 is not valid more after stamping of L1-B.
Madhu Kalra Kalra Law Firm 23720 Arlington Avenue, Ste 5 Torrance, Ca 90501 (310) 325-9012 http://www.thekalrafirm.com
You sure can board the US bound flight and present yourself for admission on B status to the CBP inspector at the airport. He or she will have your entire immigration history pop up in their screen, and of you can convince the inspector of your visit being only of a temporary nature, you will in all likelihood be admitted. Prepare yourself to answer all types of questions as to what you do, where you work, and etc. kindly note you did not "overstay" last time since you left PRIOR to your I-94's expiration date. (As you can understand from all this a consular visa is nothing more than permission to board the next US bound flight of your choice and ask or "admission" in a certain pre-approved category.. It then becomes up to the inspector whether to admit you or not . Once admitted (in the past, at least) you were given a stamped I-94 card, whose expiration date (and no longer the visa) governed the terms of your stay.
Behar Intl. Counsel 619.234.5962 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.