According to embassy policy:

来源: 于 2004-09-28 11:56:37 [旧帖] [给我悄悄话] 本文已被阅读：次

美方机构出具的正式聘书（写明工作内容、职位、聘用期限并承诺帮助进行豁免申请及转签证等内容）或入学通知书（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.