L1B to H1 and intermediate L1A. Which one will be final Visa status

I am currenlty in L1B with company A and is valid upto June 2014. Company B is ready to process H1B for me. I will be out of state from June to October 2014. If I ask to extend my current visa to company A they will file my L1A in June. Can I convert to H1 on October 1st even though my L1A is approved in June 2014 (H1 is approved in May 2014)