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We present upper critical magnetic fields data for κ(BEDT-TTF)2Cu[N(CN)2]Br (hereafter k-Br), single crystals with the magnetic field applied either or perpendicular and parallel to the conducting layers. The H-T phase diagram in these single crystals has been deduced from tunnel diode oscillator-based contactless measurements in pulsed magnetic fields up to 56 T for the inter-plane (H ∥ b) and in-plane...