H Visas: Will Your J1 Sponsor Be Informed if an Employer Applies for a H1B Visa

Hi,

I am currently on a J1 visa valid until the end of 2016 and I am not subjected to the 2-year rule.

Recently, my company offered to apply for an H1B and I checked with my sponsor if that was fine. The sponsor agency said that, both me and my employer signed an agreement were it was indicated that upon completion of the program I intended to return to my home country and not to attempt to stay in the U.S. They threaten to terminate my J1 if I even sent the H1B application. They even said that if I send the application they will get notified...I have never heard that before.

My questions are:

Is it true that if I apply for an H1B my sponsor agency will be notified or that only happens if I apply for COS instead of consular processing?

Does the USCIS report this application to the SEVIS system at all? (I'm assuming the sponsor agency has access to SEVIS)

Finally, can they really enforce such condition? I mean, if I was planning to go back home anyway and then I return with an H1B, isn't it my right to do so?

Many thanks!

H Visas: Will Your J1 Sponsor Be Informed if an Employer Applies for a H1B Visa