We present our preliminary results of the non perturbative determination of the valence mass dependent coefficients $b_A-b_P$ and $b_m$ (as well as the ratio ${Z_P/}{(Z_S Z_A)}$) entering the flavour non singlet PCAC relation in lattice QCD with $N_f=3$ dynamical flavours. We apply the method proposed in the past for quenched approximation and $N_f=2$ case, employing a set of finite-volume ALPHA configurations with Schr\"odinger functional boundary conditions, generated with $O(a)$ improved Wilson fermions and the tree-level Symanzik-improved gauge action for a range of couplings relevant for simulations at lattice spacings of about $\approx 0.09 \,$fm and below.