B1 to H1B transfer


I was laid off in February 2014, when I was on H1B. 6 weeks after that, I have left United States, and came back on B1 Visa on April. I’m still in the US and on B1 VISA. (B1 allows me to stay here 6 months)

Now I’m about to get an offer. Is my H1 still valid? (It says expires by the end of 2016. It’s also stamped on my passport) What will be the process? I think I’m not subject to H1 cap am I? Can I just transfer my status here or should I go back home?
Any help would be appreciated.
Thank you in advance.