The paper presents the following theorem: Let \(A\), \(D\), \(C\) be unital \(C^*\)-algebras, \(A\) simple and nuclear, in the relationship \(A\otimes 1_D\subset C\subset A\otimes_{\min}D\). Then \(C\) is of the form \(C= A\otimes_{\min}B\) for some \(C^*\)-subalgebra \(B\subset D\). The proof is based on two lemmas (Approximation Lemma and Invariance Lemma) which are also of indepenent interest.