Yes you can use remaining time on your H-1, even if you come back on an F-1 and change to a H-1.
I have a job offer from Europe (Sweden) which I am considering taking. I am on my first year of H1B right now. My question is if I go to Sweden to work for 1.5 years and then come back to the us on F1 to get my masters (MBA). Can I use my recapture the remining time on my H1B without going into the lottery after my masters (for example about 5 years from my original H1B time). Also will I be eligible to use my OPT after masters and also still claim my remaining H1B (5 years) without going into the lottery again?
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