For COS from L1B to H1B, how to quit current job formally

Hi, I am in a dillema and need to take a decision as soon as possible. Currently I am working with company-A with L1-B visa. They signed an agreement with me in India for notice period and job contract etc. Now I am planning to apply for H1-B and to join company-B.

1. I heard that with COS from L1 to H1, once my H1B is approved, immediately I have to quit company-A. Is it true?

 

2. In that case, if I ask company-A to give experience letter and other formal relieving documents, will they give or are they supposed to give even if I am not giving any notice period?(If I don't have time as I have to quit as soon as possible)

 

Kindly someone help me with answers as soon as possible..