Complicated H1-B transfer

I worked for company V with a H1-B.

Company A bought V and spined off several product lines of company V to the company B. I am designated to be with company B.

My questions:

(1) Is a H1-B transfer filing by company B needed ?

(2) In terms of payroll, I will be with "V"-> "A for several days"->"B",
Does A need tyo do anything about it ?