There may be transferred to and confined in the Deuel Vocational Institution any male, subject to the custody, control and discipline of the Director of Corrections, or any male, subject to the custody, control and discipline of the Youth Authority who has been committed to the Youth Authority under the provisions of Section 1731.5 of the Welfare and Institutions Code, who the Director of Corrections or Youth Authority, as the case may be, believes will be benefited by confinement in such an institution.