unfortunately yes,
Labor Certification is tied to company, you husband is only the benificaery. so he has to start green card process from scratch. Green card is job in future so only condition is if his formal employee want to continue green card process then even though your husband working with differnt company his green card filed with old company. only thing is he has to work with old company once his green card approve, and he won't be able to use any other benifit like 7th year of green card, and/ or poratabilty laws.