Shape theory is employed to show, for any compact polyhedra X, Y and any continuous maps a: \(X\to X\), b: \(Y\to Y\), that if the respective shift maps \(\sigma_ a\), \(\sigma_ b\) on the simple inverse limits \(\Sigma_ a=\lim_{\leftarrow}(X,a)\), \(\Sigma_ b=\lim_{\leftarrow}(Y,b)\) are topologically conjugate, then a, b are shift equivalent in homotopy.