In this contribution we study the problem of finding a Lyapunov matrix for neutral-type systems with distributed delay and exponential kernel. In previous works an attempt was made to reduce this problem to the computation of solutions to an auxiliary delay-free system with boundary conditions. In this paper we propose new boundary conditions allowing a significant extension of existing results. It is established that the new auxiliary boundary value problem has a unique solution if and only if there exists a unique Lyapunov matrix.