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In \cite{DvZa3}, we started the investigation of pseudo MV-algebras withsquare roots. In the present paper, the main aim is to continue to study thestructure of pseudo MV-algebras with square roots focusing on their newcharacterizations. The paper is divided into two parts. In the first part, weinvestigate the relationship between a pseudo MV-algebra with square root andits corresponding unital $\ell$-group in the scene of two-divisibility.  In the present second part, we find some conditions under which a particularclass of pseudo MV-algebras can be embedded into pseudo MV-algebras with squareroots. We introduce and investigate the concepts of a strict square root of apseudo MV-algebra and a square root closure, and we compare both notions. Weshow that each MV-algebra has a square root closure. Finally, using the squareroot of individual elements of a pseudo MV-algebra, we find the greatestsubalgebra of a special pseudo MV-algebra with weak square root.

Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures