This study is motivated by the puzzling enhanced production of multi-strange hadrons observed for the first time by the ALICE Collaboration in high-multiplicity pp-collisions at at the LHC. We investigate this effect of strangeness enhancement in pp-collisions in the framework of the MC event generator PYTHIA 8 where the collectivity processes are taken into account by the formation of a so-called flavour rope. The latter is hadronized with a larger effective string tension providing the increase of strangeness yield. This concept of the flavour rope, as a source of multi-strange hadrons, extended in rapidity, is being tested by the study of so called long-range correlations (LRC) between the average transverse momentum p_T and multiplicity n for charged particles containing strange quarks produced in high energy pp-collisions.The dependencies of correlation coefficients b_n-n, b_PT-n and b_PT-PT on the gap between forward and backward pseudorapidity windows, and on the width of the forward pseudorapidity windows, are studied and the results are discussed.