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Method of moments (MoM) solutions of electromagnetic surface integral equations provide the desired amplitudes of the equivalent surface currents on the Huygens' surfaces around the involved objects, where the solution process is nowadays routinely accelerated by fast integral methods such as the multilevel fast multipole method (MLFMM). Computation of radiated or scattered electromagnetic fields produced by these currents requires integration over the Huygens' surfaces and can easily become extremely time-consuming for large numbers of observation points. In this contribution, integration of electromagnetic near-fields is accelerated by a postprocessing MLFMM approach, where near-field and far-field translations are combined in order to achieve optimum performance. The proposed approach has been applied in the postprocessing stage of a finite element boundary integral (FEBI) method with fast integral equation solution by MLFMM, saving a large amount of postprocessing computation time. The formulation of the proposed acceleration is presented and numerical results are shown.