According to embassy policy:

回答: Yes you need to show offerwaiverdone2004-09-28 09:45:00

美方機構出具的正式聘書(寫明工作內容、職位、聘用期限並承諾幫助進行豁免申請及轉簽證等內容)或入學通知書(I-20表)。

So if you want to chang to F1, you need to show them I-20. Overall you need hard evidence that you do have a place to go after your J-1 ends.

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