How you will prepare a budget after award of contract especially in Oil and Gas field? Who will prepare the budget?

Working (bid documents) is already available. People who prepared the bid and remained involved in the contract negotiations till the finalization of the contract are the best people to prepare the budget. If the project control manager was one of them he shall take the ownership. Otherwise, all the working and information can be handed over to the project manager and project control manager who can take the ownership and carry forward the work from that stage.