This work investigates the convergence of the EM approximation for neutral-type stochastic FDEs with infinite delay in the space Cu. To ensure numerical accuracy and stability for systems with memory effects, we extend the analysis to demonstrate the squared mean convergence of the EM scheme to the exact solution under Lipschitz conditions. Asker’s work on distribution stability is expanded upon here. A numerical illustration of the impact of time step size on accuracy empirically supported the theoretical conclusions.