(Abridged) We present our VLT/FORS1 deep spectroscopic observations of the gravitationally lensed quasar SDSS J0924+0219, as well as archival HST/NICMOS and ACS images of the same object. The two-epoch spectra, obtained in the Multi Object Spectroscopy (MOS) mode, allow for very accurate flux calibration, spatial deconvolution of the data, and provide the redshift of the lensing galaxy z=0.394 +/- 0.001. These spectra, taken 15 days apart, show only slight continuum variations, while the broad emission lines display obvious changes in the red wing of the Mg II line, in the Fe II bands, and in the central part of the C III] line. Even though variations in the line profiles are present, we do not see any significant differences between the continuum and emission line flux ratios of images A and B of the quasar. Spatial deconvolution of the HST images reveals a double Einstein ring. One ring corresponds to the lensed quasar host galaxy at z=1.524 and a second bluer one, is the image either of a star-forming region in the host galaxy, or of another unrelated lower redshift object. We find that a broad range of lens models gives a satisfactory fit to the data. However, they predict very different time delays, making SDSS J0924+0219 an object of particular interest for photometric monitoring. In addition, the lens models reconstructed using exclusively the constraints from the Einstein rings, or using exclusively the astrometry of the quasar images, are not compatible. This suggests that substructures play an important role in SDSS J0924+0219.
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