We report on the discovery of a rapidly corotating stellar and gas component in the nucleus of the shell elliptical NGC 2865. The stellar component extends ~ 0.51 h_100^-1 kpc along the major axis, and shows depressed velocity dispersion and absorption-line profiles skewed in the opposite sense to the mean velocity. Associated with it is a young stellar population with enhanced Hβ, lowered Mg, and the same Fe indices relative to the underlying elliptical. Its recent star formation history is constrained by considering `bulge+burst' models under four physically motivated scenarios, using evolutionary population synthesis. Scenarios in which the nuclear component is formed over a Hubble time or recently from continuous gas inflow are ruled out. A recent starburst can satisfy observational constraints only if its population has metallicity 2.5-6.3 times that of the bulge. The nuclear iron-to-magnesium index ratio can be explained by a temperature effect in the atmospheres of stars at main-sequence turn-offs between A3 and F4, during which the Fe indices of the burst population are high enough to compensate for dilution effects. It is therefore possible to modify line-index ratios (and hence the inferred abundance ratio) simply by the presence of a young population with the same abundance. The high metallicity requirement suggests self-enrichment, and a burst duration longer than the SN II feedback time-scale. No solution exists for bursts longer than 0.4 Gyr. Burst age estimates of 0.4-1.7 Gyr are larger than that for the shells (0.24 Gyr), assuming phase-wrapping. No starburst is required if the nuclear component is composed of stars with Fe abundance enhanced by ~0.08 dex relative to the underlying elliptical, which are accreted by an event which truncated the star formation. This relies on the abundance differences between giant ellipticals and spirals. The age estimates of 0.1-0.4 Gyr in this scenario are in closer agreement with those for phase-wrapped shells. Our results argue for a gas-rich accretion or merger origin for the shells and kinematic subcomponent in NGC 2865. Arguments based on stellar populations and gas dynamics suggest that one of the progenitors is probably an Sb or Sc spiral. We demonstrate that despite the age and metallicity degeneracy of the underlying elliptical, the age and metallicity of the kinematic subcomponent can be constrained. This work strengthens the link between kinematically distinct cores (KDCs) and shells, and demonstrates that a KDC can be formed from a late merger.