We present deep I-band imaging (NOT-ALFOSC) and spectroscopic (GTC-OSIRIS) observations of the gravitational lens system SDSS J1339+1310. This consists of two images of a lensed quasar, A and B, and a lensing galaxy G between the two quasar images. Our observations led to the following main results: (1) We obtained new accurate positions for B and G (relative to A), as well as structure parameters for the light distribution of G. The new position angle for G is separated by ∼50 • from the previously determined value. (2) The spectrum of G is typical for early-type galaxies, and we measured its redshift (0.609 ± 0.001) for the first time. (3) We determined the flux ratio B/A for the cores of the emission lines in the two quasar spectra. They were used to constrain the macrolens flux ratio M BA and dust extinction parameters. (4) The continuum flux ratio was appropriately corrected to obtain the microlensing magnification ratio of the continuum μ BA . This μ BA indicates that B is amplified (relative to A) by a factor of about 3−5, with larger amplifications at shorter wavelengths. The observed microlensing chromaticity coincides with a sharp drop in the r-band flux of B.(5) We reconstructed the lensing mass from the new observational constraints on the relative astrometry, M BA and the luminous structure of G. We also used the redshift of G to predict the time delay between quasar images (43 ± 5 d, A is leading).