The Maximum Satisfiability problem (MaxSAT) is a major optimization challenge with numerous practical applications. In recent MaxSAT evaluations, most MaxSAT solvers have incorporated an Integer Linear Programming (ILP) solver into their portfolios. However, a good portfolio strategy requires a lot of tuning work and is limited to the profiling benchmark. This paper proposes a methodology to fully integrate ILP preprocessing techniques into the MaxSAT solving pipeline and investigates the impact on the top-performing MaxSAT solvers. Experimental results show that our approach helps to improve 5 out of 6 state-of-the-art MaxSAT solvers, especially for WMaxCDCLOpenWbo1200, the winner of the MaxSAT evaluation 2024 on the unweighted track, which is able to solve 15 additional instances using our methodology.