An uniform LP duality is an useful property of conic matrix systems. A consistent linear conic optimization problem yields uniform LP duality if for any linear cost function, for which the primal problem has finite optimal value, the corresponding Lagrange dual problem is attainable and the duality gap vanishes. In this paper, we establish new necessary and sufficient conditions guaranteing the uniform LP duality for linear problems of Copositive Programming and formulate these conditions in different equivalent forms. The main results are obtained using an approach developed in previous papers of the authors and based on a concept of immobile indices that permits alternative representations of the set of feasible solutions.
