By simply having the prospective employer file an H-1B petition on April 1, with an employment start date of October 1 (there are no H-1B visas available before then) and hoping that your employer's H-1B petition will end up being selected in the likely "lottery" for H-1Bs, since if the past 2 years are a guide, there'll be many more H-1Bs filed than H-1B visa numbers available.
If your "Work & Travel" J-1 were to expire anytime soon, the prospective employer better file another J-1 for "internship" on your behalf and even an H-3 "training" visa, if that were feasible at all. Consult with an experienced immigration attorney to learn more and receive custom-tailored advice.
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.
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