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We report the first demonstration of Raman amplification in a fiber of a single Bessel-like higher order mode using a multimode pump source. We amplify the LP_08-mode with a 559-µm^2 effective mode area at a signal wavelength of 1115 nm in a pure-silica-core step-index fiber. A maximum of 18 dB average power gain is achieved in a 9-m long gain fiber, with output pulse energy of 115 µJ. The Raman pump source comprises a pulsed 1060 nm ytterbium-doped fiber amplifier with V-value ~30, which is matched to the Raman gain fiber. The pump depletion as averaged over the signal pulses reaches 36.7%. The conversion of power from the multimode pump into the signal mode demonstrates the potential for efficient brightness enhancement with low amplification-induced signal mode purity degradation.