Scattered linear sets of PG(3,qn) generated by collineations between stars of lines

Let A and B be two points of PG(3,qn) and let Φ be a collineation between the stars of lines with vertices A and B that fixes the line AB. In this paper we prove that the set C of points of intersection of corresponding lines under Φ, under the hypothesis that C generates PG(3,qn), is either the union of two degenerate CFm-sets in two planes through the line AB (see Donati and Durante, 2014) or the union of a scattered GF(q)-linear set of rank n+2 with the line AB. We also determine the intersection configurations of two scattered GF(q)-linear sets of rank n+2 of PG(3,qn) both meeting the line AB in a GF(q)-linear set of pseudoregulus type with transversal points A and B.