The planetary system around the naked-eye star v² Lupi (HD 136352; TOI-2011) is composed of three exoplanets with masses of 4.7, 11.2, and 8.6 Earth masses (M_⊕). The TESS and CHEOPS missions revealed that all three planets are transiting and have radii straddling the radius gap separating volatile-rich and volatile-poor super-earths. Only a partial transit of planet d had been covered so we re-observed an inferior conjunction of the long-period 8.6 M_⊕ exoplanet v² Lup d with the CHEOPS space telescope. We confirmed its transiting nature by covering its whole 9.1 h transit for the first time. We refined the planet transit ephemeris to P = 107.1361_−0.0022^+0.0019 days and T_c = 2459009.7759_−0.0096^+0.0101 BJD_TDB, improving by ~40 times on the previously reported transit timing uncertainty. This refined ephemeris will enable further follow-up of this outstanding long-period transiting planet to search for atmospheric signatures or explore the planet’s Hill sphere in search for an exomoon. In fact, the CHEOPS observations also cover the transit of a large fraction of the planet’s Hill sphere, which is as large as the Earth’s, opening the tantalising possibility of catching transiting exomoons. We conducted a search for exomoon signals in this single-epoch light curve but found no conclusive photometric signature of additional transiting bodies larger than Mars. Yet, only a sustained follow-up of v² Lup d transits will warrant a comprehensive search for a moon around this outstanding exoplanet.