We describe a fiber Raman amplifier for nanosecond and sub-nanosecond pulses centered around 1260 nm. The amplification takes place inside a 4.5-m-long polarization-maintaining phosphorus-doped fiber, pumped at 1080 nm by 3-ns-long pulses with a repetition rate of 200 kHz and up to 1.75 kW peak power. The input seed pulses are of sub-mW peak-power and minimal duration of 0.25 ns, carved out of a continuous-wave laser with sub-MHz linewidth. We obtain linearly polarized output pulses with peak powers of up to 1.4 kW, corresponding to peak-power conversion efficiency of over 80%. An ultrahigh small signal gain of 90 dB is achieved, and the signal-to-noise ratio 3 dB below the saturation power is above 20 dB. No significant temporal and spectral broadening is observed for output pulses up to 400 W peak power, and broadening at higher powers can be reduced by phase modulation of the seed pulse. Thus, nearly-transform-limited pulses with peak power up to 1 kW are obtained. Finally, we demonstrate the generation of pulses with controllable frequency chirp, pulses with variable width, and double pulses. This amplifier is thus suitable for coherent control of narrow atomic resonances, especially for the fast and coherent excitation of rubidium atoms to Rydberg states. These abilities open the way towards several important applications in quantum non-linear optics.