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We present spectroscopy and laser guide star adaptive optics (LGSAO) imagesof the doubly imaged lensed quasar SDSS J1206+4332. We revise the deflectorredshift proposed previously to $z_{d}=0.745,$ and measure for the first timeits velocity dispersion $\sigma=(290\pm30)$ km/s. The LGSAO data show thelensed quasar host galaxy stretching over the astroid caustic thus forming anextra pair of merging images, which was previously thought to be an unrelatedgalaxy in seeing limited data. Owing to the peculiar geometry, the lens acts asa natural coronagraph on the broad-line region of the quasar so that onlynarrow [O III] emission is found in the fold arc. We use the data toreconstruct the source structure and deflector potential, including nearbyperturbers. We reconstruct the point-spread function (PSF) from the quasarimages themselves, since no additional point source is present in the field ofview. From gravitational lensing and stellar dynamics, we find the slope of thetotal mass density profile to be $\gamma^{\prime}=-\log\rho/\log r=1.93\pm0.09.$ We discuss the potential of SDSS J1206+4332 for measuring timedelay distance (and thus H$_0$ and other cosmological parameters), or as astandard ruler, in combination with the time delay published by the COSMOGRAILcollaboration. We conclude that this system is very promising for cosmography.However, in order to achieve competitive precision and accuracy, an independentcharacterization of the PSF is needed. Spatially resolved kinematics of thedeflector would reduce the uncertainties further. Both are within the reach ofcurrent observational facilities.

High resolution imaging and spectroscopy of the gravitational lens  SDSSJ1206+4332: a natural coronagraph at $z=1.789$ and a standard ruler at  $z=0.745$