Can I transfer from H1 to L1B while in US

Hi All,

 I am in the last year of my 6yrs period in US. Iniyially I was on L1 for a year and 4 years on H1. This is my 5th yr on H1 and 6th yr in US though it was not a continuous stay. I have my H1 797 valid until Sep 2013 and am in US right now. Meanwhile Can I transfer this H1 to L1 so my employer can sponser me a GC on L1? I have already worked for an year for the same company in India last year. Also if this is not an option can my employer or any other company sponser me a fresh H1 in next year qouta while I am in US? What are my chances of getting either of the 2 approved? Do I have to get my new visa stamped before starting work with new status?

Please let me know. Any help is highly appreciated.

Thanks

To clarify, L1 has two types. L1A and l1B

  1. L1A - is for manager and person can stay for 7 yrs in US

  2. L1B - is for specialized knowledge and valid only for 5 ys.

If you are elligible for L1A then yes; your employer can do that.