  We report on the results of a 4-year timing campaign of PSR~J2222$-0137$, a
2.44-day binary pulsar with a massive white dwarf (WD) companion, with the
Nan\c{c}ay, Effelsberg and Lovell radio telescopes. Using the Shapiro delay for
this system, we find a pulsar mass $m_{p}=1.76,\pm\,0.06,M_\odot$ and a WD mass
$m_{c}\,=\,1.293\,\pm\,0.025\, M_\odot$. We also measure the rate of advance of
periastron for this system, which is marginally consistent with the GR
prediction for these masses. The short lifetime of the massive WD progenitor
star led to a rapid X-ray binary phase with little ($< \, 10^{-2} \, M_\odot$)
mass accretion onto the neutron star (NS); hence, the current pulsar mass is,
within uncertainties, its birth mass; the largest measured to date. We discuss
the discrepancy with previous mass measurements for this system; we conclude
that the measurements presented here are likely to be more accurate. Finally,
we highlight the usefulness of this system for testing alternative theories of
gravity by tightly constraining the presence of dipolar radiation. This is of
particular importance for certain aspects of strong-field gravity, like
spontaneous scalarization, since the mass of PSR~J2222$-0137$ puts that system
into a poorly tested parameter range.
