The implicative conditional strengthens the strict conditional and circumvents the paradoxes of the latter, all by remaining modally interpretable. This paper extends the analysis from Raidl and Gomes (2025) where Import (IM) and Export (EX) are analyzed for \({{\,\mathrm{\Rightarrow }\,}}\) , as well as possibilistic versions, where either the possibility of the antecedent of the consequent conditional (P1X) or the consequent of it (P2X) or both (PPX) are added as antecedent of the principle (X= IM or EX). In reflexive Kripke models, \({{\,\mathrm{\Rightarrow }\,}}\) only validates PPIM. Thus no Gibbardian collapse arises, i.e. \({{\,\mathrm{\Rightarrow }\,}}\) remains distinct from material implication, since the collapse theorem requires at least EX and Simplification (SI), which are both invalid for \({{\,\mathrm{\Rightarrow }\,}}\) . Here I investigate the other principles and their modal counterparts. I show that, in reflexive Kripke models, P1IM corresponds to the modal axiom 4, and IM to 4 together with the provability axiom Grz. On the other hand, in Kripke models, P2EX (and hence PPEX) corresponds to the modal axiom 5 together with shift-discreteness \({{\,\mathrm{\square }\,}}(A \supset {{\,\mathrm{\square }\,}}A)\) . It is then easily shown that all Exportations imply the collapse . Hence, although there are non-trivial ways to validate Importation(s), without implying a collapse, there is no non-trivial way for \({{\,\mathrm{\Rightarrow }\,}}\) to validate Exportation from a normal modal logic perspective.