We report the detection of CO(J=3-2) line emission in the strongly-lensed submillimeter galaxy (SMG) SMM J0939+8315 at z=2.221, using the Combined Array for Research in Millimeter-wave Astronomy. SMM J0939+8315 hosts a type-2 quasar, and is gravitationally lensed by the radio galaxy 3C220.3 and its companion galaxy at z=0.685. The 104 GHz continuum emission underlying the CO line is detected toward 3C220.3 with an integrated flux density of S_cont = 7.4 +/- 1.4 mJy. Using the CO(J=3-2) line intensity of I_(CO(3-2)) = (12.6 +/- 2.0) Jy km s^-1, we derive a lensing- and excitation-corrected CO line luminosity of L(CO(3-2)) = (3.4 +/- 0.7) x 10^10 (10.1/mu_L) K km s^-1 pc^2 for the SMG, where mu_L is the lensing magnification factor inferred from our lens modeling. This translates to a molecular gas mass of M_gas = (2.7 +/- 0.6) x 10^10 (10.1/mu_L) Msun. Fitting spectral energy distribution models to the (sub)-millimeter data of this SMG yields a dust temperature of T = 63.1^{+1.1}_{-1.3} K, a dust mass of M_dust = (5.2 +/- 2.1) x 10^8 (10.1/mu_L) Msun, and a total infrared luminosity of L_IR = (9.1 +/- 1.2) x 10^12 (10.1/mu_L) Lsun. We find that the properties of the interstellar medium of SMM J0939+8315 overlap with both SMGs and type-2 quasars. Hence, SMM J0939+8315 may be transitioning from a star-bursting phase to an unobscured quasar phase as described by the evolutionary link model, according to which this system may represent an intermediate stage in the evolution of present-day galaxies at an earlier epoch.