We have simulated the invasion of a polyelectrolyte complex made of a polycation chain and a polyanion chain, by another longer polyanion chain, using the coarse-grained united atom model for the chains and the Langevin dynamics methodology. Our simulations reveal many intricate details of the substitution reaction in terms of conformational changes of the chains and competition between the invading chain and the chain being displaced for the common complementary chain. We show that the invading chain is required to be sufficiently longer than the chain being displaced for effecting the substitution. Yet, having the invading chain to be longer than a certain threshold value does not reduce the substitution time much further. While most of the simulations were carried out in salt-free conditions, we show that presence of salt facilitates the substitution reaction and reduces the substitution time. Analysis of our data shows that the dominant driving force for the substitution process involving polyelectrolytes lies in the release of counterions during the substitution.