Cap-exempt to Cap-subject: Eligible for Masters quota?

[dta]

Hello, 

I'm an MS STEM student at a private not-for-profit accredited University.

The University is will to hire me under Cap-exempt H1-B.

If, in the future, I decide to move to a for-profit organization (which will be cap-eligible), can I still make use of the Masters' quota of 20,000 in the lottery?

Is there a time-limit for being qualified to use it? Will it matter that when I apply for it I will be on H1-B and not on F1?

Please advise.
Thank you.