Its clear company A wont be sponsoring H1 for you. Also I am pretty sure company B wont be sponsoring H1 either (immediately)as it is a temp to hire contractor position. Once u get full time in company B you might get H1 sponsorship from company B. so for now start working for company B and fig out if there is chances of getting h1 from them, chances of getting rid of company A by getting full time in company B.

your situation is like you got job at ABC company(company B) through Robert half technology(company A) company A wont sponsor h1 and dont know abt company B right away. nothing to loose as of right now as u dont have H1 yet