The Poisson multi-Bernoulli mixture (PMBM) filter is extended for distributed implementation using a wireless sensor network. At the core of the proposed networking approach, the PMBM posterior is decomposed into two parts corresponding to the undetected and detected targets, respectively. Fusion is motivated to be performed with regard to the latter only which is represented by MBM based on a distributed flooding algorithm for internode communication, which iteratively shares the MBMs between neighbor sensors. Then, a suboptimal “best-fit-ofmixture” principle is followed at each local sensor to find a MBM that best fits the mixture of MBMs aggregated from distinct sensors, leading to an arithmetic average (AA) of these MBMs. We prove the exact closure of the MBM-AA fusion and discuss its sub-optimality and limitations. Simulation demonstrates the effectiveness and limitations of our approach.