Could I switch to H1B When I applying for Green Card on L1B status?

I’m working in USA under L1B now. My company will begin the Green Card applying process for me soon, but it takes long time(may be 5 or 6 years) when my L1B VISA expired. So, When I applying for Green Card on L1B status, could I switch to H1B? Can Green Card filling process cause any problem in COS L1B-H1B? If I can switch to H1B, would we have to re-do any part of the Green Card applying process? Or will whatever processes we started while on L1-B keep going after we switched to H1-B?