In this paper we present the three-dimensional dynamics of the galaxy SDSS J101345.39+011613.66, selected for its unusually strong Balmer absorption lines [W0(Hδ) = 7.5 Å]. Using the Gemini Multi-Object Spectrograph-South integral field unit (IFU) in nod+shuffle mode, we have mapped the continuum and optical absorption lines of this z = 0.1055 field galaxy. This galaxy has a disturbed morphology, with a halo of diffuse material distributed asymmetrically toward the north. Using the [O II] emission line (W0[O ] = 4.1 Å), we find that the gas and hot OB stars are offset from the older stars in the system. The gas also has a spatially extended and elongated morphology with a velocity gradient of 100 ± 20 km s-1 across 6 kpc in projection. Using the strong Hγ and Hδ absorption lines, we find that the A stars are widely distributed across the system and are not centrally concentrated, arguing that the A star population has formed in molecular clouds outside the nucleus. By cross-correlating the spectra from the data cube with an A star template, we find evidence that the A star population has a 40 km s-1 shear in the same direction as the gas. The disturbed morphology, strong color gradients, and strong Hδ and Hγ absorption lines in SDSS J101345.39 argue that this is a recent tidal interaction/merger between a passive elliptical and a star-forming galaxy. Although based on a single object, these results show that we can spatially resolve and constrain the dynamics of this short-lived (yet important) phase of galaxy formation in which the evolutionary process takes galaxies from star-forming to their quiescent end products.