The court may authorize the sheriff to whose custody a defendant is committed, to arrange with another sheriff for the employment of the offender in the latter’s county, and while so employed to be in the latter sheriff’s custody but in other respects to be and continue subject to the commitment. The cost of maintenance of such offender shall be paid by the county in which he was committed. The Department of Corrections may transfer an offender committed to it to another institution or facility of the Department subject to the approval of the committing court.