Can I be in the USA while my H1B is being processed, but my J1 has ended?

I am currently in the USA on a J1 Visa.

I might apply for an H1B this spring (April) and hopefully I can start to work by October.

However, my J1 expires in June. Does this mean that between June and October, do I have to leave the country or can I actually be here? Can I work during that time or do I have to wait for the H1 to be approved?

Thanks!

Simon

If you are on J1. there might be 2 year home country rule applicable to you. Just check that

http://travel.state.gov/visa/temp/info/info_1296.html

I am not sure if you are eligible for Cap gap - opt.

Ok, I have checked so there is no 2 year home country rule for me.

Did you answer my question if I could be here while my H1B is being processed? Could I even work during the time my visa is being processed?

Thanks!

Simon