We present high-precision radial velocities (RVels) from the HARPS-N spectrograph for HD79210 and HD79211, two M0V members of a gravitationally bound binary system. We detect a planet candidate with a period of 24.421_-0.017_^+0.016^days around HD79211 in these HARPS-N RVels, validating the planet candidate originally identified in CARMENES RVel data alone. Using HARPS-N, CARMENES, and RVels spanning a total of 25yr, we further refine the planet candidate parameters to P=24.422{+/-}0.014days, K=3.19{+/-}0.27m/s, Msini=10.6{+/-}1.2M{Earth}, and a=0.142{+/-}0.005au. We do not find any additional planet candidate signals in the data of HD79211, nor do we find any planet candidate signals in HD79210. This system adds to the number of exoplanets detected in binaries with M-dwarf members and serves as a case study for planet formation in stellar binaries.