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Let $G$ be a compact Lie group with a maximal torus $T$. Based on apresentation of the integral cohomology ring $H^{\ast}(G/T)$ of the flagmanifold $G/T$ in \cite{DZ1}we have presented in \cite{DZ2}an explicit andunified construction of the integral cohomology rings $H^{\ast}(G)$ for the$1$--connected Lie groups $G$. In this paper we extend this construction to allcompact Lie groups.

Schubert calculus and cohomology of Lie groups. Part II. Compact Lie groups