Integral field optical spectroscopy using the INTEGRAL system (complemented with Hubble Space Telescope WFPC2 imaging) is used to characterize the kinematic and ionization properties of the warm ionized gas in the ultraluminous infrared galaxy IRAS 15206+3342. These data present kinematic and morphological evidence for a tidal tail connecting the nuclear star-forming regions with a remnant stellar system located at a projected distance of 20 kpc away from the nucleus. The velocity field and the velocity dispersion map indicate the presence of gas flowing inward along the tidal tail, feeding the nuclear regions where the previously detected arc-shaped chain of young stellar clusters is forming stars at a rate of about 150 Msolar yr-1. According to theoretical models by Mihos & Hernquist, these characteristics (e.g., large gas inflows and massive starbursts) are expected during the final coalescence phase of two disk galaxies with bulges. No kinematic evidence for a second nucleus, nor for the presence of young star-forming regions located along the external parts of the tidal tail, is found, further supporting the conclusion that this system is an advanced merger of two galaxies. Furthermore, photometric and geometrical arguments indicate that the progenitors of this ultraluminous infrared system were two low-luminosity (