Context. The second legacy catalogue of Planck Sunyaev-Zeldovich (SZ) sources, hereafter PSZ2, provides the largest galaxy cluster sample selected by means of their SZ signature in a full sky survey. In order to fully characterise this PSZ2 sample for cosmological studies, all the members should be validated and the physical properties of the clusters, including mass and redshift, should be derived. However, at the time of its publication roughly 21 per cent of the 1653 PSZ2 members had no known counterpart at other wavelengths. Aims. Here, we present the second and last year of observations of our optical follow-up programme 128-MULTIPLE-16/15B (hereafter LP15), which has been developed with the aim of validating all the unidentified PSZ2 sources in the northern sky, with declination above −15°, and with no correspondence in the first Planck catalogue PSZ1. The description of the programme and the first year of observations were presented in Streblyanska et al. (2019). Methods. The LP15 programme was awarded 44 observing nights, spread over two years in the Isaac Newton Telescope (INT), the Telescopio Nazionale Galileo (TNG) and the Gran Telescopio Canarias (GTC), all at Roque de los Muchachos Observatory (La Palma). Following the same methodology described in Streblyanska et al. (2019), at the end of the LP15 programme we performed deep optical imaging for more than 200 sources with the INT, and spectroscopy for almost 100 sources with the TNG and GTC. We adopted a robust confirmation criteria based on velocity dispersion and richness estimations in order to carry out the final classification of the new galaxy clusters as the optical counterparts of the PSZ2 detections.Results. Here, we present the observations of the second year of LP15, as well as the final results of the programme. The full LP15 sample comprises 190 previously unidentified PSZ2 sources. Of those, 106 objects were studied in Streblyanska et al. (2019), while the remaining sample (except for 6 candidates) has been completed in the second year and it is discussed here. In addition to the LP15 sample, in this paper we have studied 42 additional PSZ2 objects, which were originally validated as real clusters due to their matching with a WISE or PSZ1 counterpart, but they had no measured spectroscopic redshift. In total, we have confirmed the optical counterpart for 81 PSZ2 sources after the full LP15 programme, 55 of them with new spectroscopic information. Out of those 81 sources, 40 clusters are presented in this paper. After the LP15 observational programme the purity of the PSZ2 catalogue has increased from 76.7 % originally to 86.2 %. In addition, we study the possible reasons of having false detection, and we report a clear correlation between the number of unconfirmed sources and galactic thermal dust emission.