回複：回複：回複：follow-up question: Urgent help with H1-B visa

The employer has agreed to sponsor H1-B visa application for me,

 

but I am not sure if it is OK for them to start working on the paperwork, since technically I am still in OPT period until the middle of July.

-Yes, OPT is irrelevant to H1 application. But unless your employer is a college/university or non-profit organization, you can not apply for the H1 now because there is not H1 quote available until April 2013.