To enhance the performance of micro-patterned gaseous detectors (MPGDs) to meet thechallenging requirements of future high energy physics (HEP) experiments, two-dimensional (2D)materials are attractive candidates to address the back flow of positive ions, which affectsdetector performance by distorting electric field lines. In this context, graphene is promisingto work as selective filter for ion back flow suppression, being transparent to electrons while atthe same time blocking ions. Also, graphene membranes can physically separate drift andamplification regions of the detectors, offering additional flexibility in the choice of gasmixtures and allowing independent optimizations of detector sensitivity and electronmultiplication processes. Here we present an approach to integrate graphene grown via chemicalvapor deposition (CVD) on gaseous electron multiplier (GEM) prototypes via a wet transferprocedure in order to suspend graphene over thousands of holes with 60 μm diameter and overcomethe challenges encountered due to process steps involving liquids, mostly related with thecapillary effects during drying and evaporation of them. In order to overcome the risk of damagingthe membrane and decreasing the yield of suspended 2D material membranes, critical point dryer(CPD) and inverted floating method (IFM) procedures are investigated. In addition to thenecessity to cover the full holes in the active area, polymeric residuals have to be minimized inorder to evaluate the graphene transparency at the electron energies (i.e., < 15 eV) typicallyobtained in the operating conditions, measurements in these energy ranges are still not deeplyinvestigated.