The following is the main result of the paper. Let \(X\) be a subspace of \(\ell_1\) such that (i) \(\ell_1/X\) has an unconditional finite-dimensional decomposition and (ii) every operator \(T:X \to C(K)\) can be extended to \(\ell_1\). Then there is an automorphism \(\tau\) of \(\ell_1\) such that \(\tau (X)\) is weak\(^*\) -closed. This may be viewed as a converse to a statement in W. B. Johnson and M. Zippin [Stud. Math. 117, 43-55 (1995; Zbl 0851.46017)].