@War***
VISAS are stickers and can't be transferred to a new passport.
You show BOTH passports when you exit the country, they will note you hold a valid Non-O visa in passport xxx in the new passport and stamp you OUT on the new one and then when you stamp back in you show BOTH passports again to get stamped in on the new passport.
You do this (showing BOTH passports) when you exit/re-enter until the VISA in the old passport runs out.