In the case of Partnership, register or create a reconsecuted partnership deed in favour of two sons. In the case of proprietorship, change the ownership from all deeds (Bank, rent agreements) by executing by a settlement deed.
In the case of company make a resignation letter from the company and transfer your fathers share to both sons as per his wish and file necessary application for transfer the share before Registrar of company with help of Charted accountant or company secretary