Second Lottery: Filing H1-B for cap 2021 COS


My H1B got picked up in the second lottery but with a different employer. I am currently on F1 visa STEM OPT working with employer A, but the H1 registration got picked up with employer B. I would like to ask can I file for the H1B COS and then transfer the project from employer A to employer B if the H1B is approved ?