An alternative construction of the invariant of homology three spheres valued in a completion of an integral polynomial ring associated to each quantized complex simple Lie algebra by Habiro and Lê [Unified quantum invariants for integral homology spheres associated with simple Lie algebras, Geom. Topol. 20 (2016) 2687–2835, doi:10.2140/gt.2016.20.2687, arXiv:1503:03549v1] is given.