Fabrikant., et al., in the paper "The complexity of pure Nash equilibria" (http://kunaltalwar.org/papers/purenash.pdf) show that finding a pure Nash equilibrium (PNE) in a Congestion game is a PLS-complete problem. Moreover, it is known that every exact Potential game has an equivalent Congestion game with the same potential function (Theorem 6.12, here: http://www.math.tau.ac.il/~mansour/course_games/scribe/lecture6.pdf).
Then, is it correct to say finding a PNE for an exact Potential game is a PLS-complete problem as well?
Finding PNE in exact potential games is PLS-complete, though maybe not by the logic you mentioned. You can prove this by PLS - reducing the Weighted Satisfiability problem (A PLS-complete problem) to the problem of finding a PNE for an exact potential game (EPG) - which proves that finding PNE in EPG is PLS-Hard. Then trivially, finding PNE in EPG is in PLS, hence this problem is PLS-complete.
Minor flaw in your argument: Your argument is correct (but it has to be verified.). Assuming that Fabrikant et al show that CG (congestion game) is PLS-complete, we know that there is an isomorphism between a CG and an EPG. Now in order to state that EPG is PLS-complete, you have to show that the 'isomorphism functions' are polynomial time computable - which they are, but it still needs to be shown.