Don't I need to do H-1B transf

I'm H-1B in company A. My company A was bought by company B recently, so I'm now working for company B as the same job title and duty. I think I need to do H-1B transfer. But the immigration lawyer of company B said there's no need to do H-1B transfer. For such company merge case, they only need to do some document backup inside company. Is that true? Do I need do H-1B transfer? Thanks for your help