The partial maximum satisfiability problem is an important variant of the satisfiability problem. It can handle both hard and soft constraints simultaneously and thus can model a wide range of realistic problems. Local search solvers are the mainstream method to find high-quality solutions to the partial maximum satisfiability problem, and they rely on initial data states of problem instances. Aiming at the initial solution generation process of a local search solver, namely, SATLike3.0, this study proposes an improvement strategy that gives priority to satisfy the hard constraints, and the obtained algorithm is dubbed HFCRP-F. The algorithm works on the stages of initial solution construction and initial weight configuration, including propagating unassigned variables in unsatisfied hard constraints and adding initial weights to constraints based on found solutions, so as to guide the subsequent local search process. HFCRP-F and SATLike3.0 are tested by using data sets from MaxSAT Evaluation 2018–2021. The results reveal that HFCRP-F performs much better than SATLike3.0 in processing weighted instances and shows nearly the same performance as SATLike3.0 in processing non-weighted instances.