L1B to H1B Visa

I am currently with my L1B working for (XXX). In parallel I also applied for my H1B with a third party employer got it selected and petition got approved, the same H1B I applied in Premium for stamping and went on stamping and received 221 g blue slip, I also got an opportunity with my current employer(XXX) to travel to USA. I got an email from consulate requesting for couple of documents to approve my H1B, employer said he may not be able to provide those documents. In return he also said me to withdraw my current application.

I need to know how I can hold my H1B ? and also is it possible to COS from L1B to H1B?