The computation of the displacement enrichment within the original version of the XPFM relies on detecting so-called crack points and defining a direction perpendicular to the crack path. This negates, to some extent, the advantage of the non-discrete approximation of the crack in the phase-field method. In the improved version of the XPFM framework presented in part 1 of this contribution, the displacement field ansatz relies on modified shape-functions which are calculated for each enriched element on a sub-problem. Since it is directly coupled to the stiffness degradation, the detailed and discrete location of the crack is not required, thereby preserving the advantage of the smeared representation of the crack. As a result, the method is more versatile than its predecessor and can more easily account for crack branching and coalescence. In this part 2 of the contribution, the specific formulation of the sub-problem is presented. The modified shape-functions are calculated from a phase-field dependent distortion of the enriched elements’ reference space, which is obtained as a solution from a stiffness-degradation, and, therefore, phase-field dependent Laplacean problem. Here, EAS-type elements are employed to prevent an overly stiff behaviour of the solution due to locking. Specific boundary conditions have to be incorporated to keep the continuity of the solution over the enriched elements’ edges and to ensure the adherence to coordinate properties. Since the meshes of the sub-problem are standardized across different resolutions, the system of equations for each enriched element can be assembled and solved directly, without invoking an additional finite-element instance. This allows for highly efficient computation. The element-wise treatment makes the approach well-suited for parallelization. In this contribution, two sub-problem formulations and various mesh resolutions are tested and compared through numerical simulations. The performance of the proposed method is shown with further examples.