The identification of Hawkes-like processes can pose significant challenges. Despite substantial amounts of data, standard estimation methods show significant bias or fail to converge. To overcome these issues, we propose an alternative approach based on an expectation-maximization algorithm, which instrumentalizes the internal branching structure of the process, thus improving convergence behavior. Furthermore, we show that our method provides a tight lower bound for maximum-likelihood estimates. The approach is discussed in the context of a practical application, namely the collection of outstanding unsecured consumer debt.