mandatory any more, at least, in light nuclei. We can use a kind of $ab$-$initio$ cluster model which employs more realistic cluster wave functions with realistic interactions. Therefore, it is interesting to see the difference between the $ab$-$initio$ reaction calculations with a tensor term and the conventional cluster model calculations without a tensor term in few-body systems. The microscopic $R$-matrix method (MRM) with a cluster model (GCM or RGM) has been applied to studies of many nuclei [@baye77; @kanada85; @arai01; @desc10]. It is now used in $ab$ $initio$ descriptions of collisions [@navratil09]. We have also applied the MRM to the $h$+$p$ scattering problem with more realistic cluster wave functions by using a realistic interaction [@arai10]. The Gaussian basis functions for the expansion of the cluster wave functions are chosen by a technique of the SVM [@book]. In the MRM, as will be shown later, the relative wave function between clusters ($a$ and $b$) is connected to the boundary condition at a channel radius. The problem is how to calculate the matrix elements. In this paper, we develop a method called the Triple Global Vector Representation method (TGVR), by which we calculate the matrix elements in a unified way. Although we 