Don't understand what you think.

Firstly, you need to apply J1 waiver before changing any visa, such as H1. J1 waiver is your business, your university cannot help much. But they must write you a letter to support your future work after your J1 expired. This letter is for Chinese embassy only and you can tell them it is not a promise. But if you haven't this letter, it is hard for you to get this J1 waive.

After you get your J1 waive (maybe need half year to 1 year), you can change your visa to H1. Before you get this, you must keep your J1.