This paper continues the investigations of the authors in part I [J. Pure Appl. Algebra 214, No. 3, 251-268 (2010; Zbl 1211.20016)], where are defined the notions partial actions, partial projective representations and twisted partial actions of a group \(G\) over a field \(K\). The interactions between these notions here are treated in a categorical language. With each partial projective representation of \(G\) is associated a factor set \(\sigma=\{\sigma(x,y)\in K\mid x,y\in G\}\). In the case of a finite group \(G\), structural results for \(\sigma\) are obtained in terms of elementary partial actions. For arbitrary groups is used the structure of Exel's semigroups. A complete characterization of \(\sigma\) in this case is obtained for algebraically closed fields.