  Aims. We provide an in-depth analysis of the COSMOS-Web ring, an Einstein
ring at z=2 that we serendipitously discovered in the COSMOS-Web survey and
possibly the most distant lens discovered to date.
  Methods. We extract the visible and NIR photometry from more than 25 bands
and we derive the photometric redshifts and physical properties of both the
lens and the source with three different SED fitting codes. Using JWST/NIRCam
images, we also produce two lens models to (i) recover the total mass of the
lens, (ii) derive the magnification of the system, (iii) reconstruct the
morphology of the lensed source, and (iv) measure the slope of the total mass
density profile of the lens.
  Results. The lens is a very massive and quiescent (sSFR < 10^(-13) yr-1)
elliptical galaxy at z = 2.02 \pm 0.02 with a total mass Mtot(<thetaE) = (3.66
\pm 0.36) x 10^11 Msun and a stellar mass M* = (1.37 \pm 0.14) x 10^11 Msun.
Compared to SHMRs from the literature, we find that the total mass is
consistent with the presence of a DM halo of mass Mh = 1.09^(+1.46)_(-0.57) x
10^13 Msun. In addition, the background source is a M* = (1.26 \pm 0.17) x
10^10 Msun star-forming galaxy (SFR=(78 \pm 15) Msun/yr) at z = 5.48 \pm 0.06.
Its reconstructed morphology shows two components with different colors. Dust
attenuation values from SED fitting and nearby detections in the FIR also
suggest it could be partially dust-obscured.
  Conclusions. We find the lens at z=2. Its total, stellar, and DM halo masses
are consistent within the Einstein ring, so we do not need any unexpected
changes in our description of the lens (e.g. change its IMF or include a
non-negligible gas contribution). The most likely solution for the lensed
source is at z = 5.5. Its reconstructed morphology is complex and highly
wavelength dependent, possibly because it is a merger or a main sequence galaxy
with a heterogeneous dust distribution.
