In order to definitely prove the claim by Claeskens et al. (1996A&A...305L...9C) that J03.13 is a doubly imaged quasar, WFPC2 direct imaging and FOS spectroscopy of this compact system have been obtained with HST. These textbook case observations clearly show that J03.13 consists of two point-like images separated by 0.849"+/-0.001" with a magnitude difference of 2.14+/-0.03 in V and I. We see no trace of a lensing galaxy. From the FOS observations, we find that J03.13 A and B have identical spectra within the measurement uncertainties. The data also show that spectroscopic contamination of B by A is negligible. We do confirm the redshift z=2.545 for J03.13 A and B (emission-lines due to Ly-β λ1025 and O VI λλ1031, 1037 are also detected), first derived from an unresolved ground-based spectrum of the two components by Claeskens et al. We also find that the absorption line system at z=2.344 (CIV and Ly-α) is present in the spectra of A and B. On the contrary, the absorption line system at z=1.085 (MgII) is only present in the spectrum of J03.13 A. If this latter system is associated with the lens, we may expect that image A consists of two radially merging images with a very small angular separation. From the WFPC2 imagery, we can rule out the presence of a third component fainter than A by up to 5.2mag. with an angular separation >=0.13".