If a person working in a company in 17 month OPT extended period has to transfer job in new company , does the new company has to be E-verified?

Secondly,

If (say in June) person's h1b is approved applying from one company and the sameperson wants to transfer job in other company on June/July ...is it possible to transfer..he will be in opt period till october and want to take on H1B.