Addendum to "The $\widehat{A}$-genus of $S^1$-manifolds with finite second homotopy group"

In C. R. Math. Acad. Sci. Paris 348 (2010) pp. 283–285 (arXiv:0811.0840) we constructed examples of $S^1$-manifolds with finite second homotopy group and non-vanishing $\widehat{A}$-genus. The reasoning was based on an equivariant surgery lemma which only holds under additional assumptions. To remedy the situation we give a construction using explicit equivariant surgeries.