A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λ n via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ : Z n → G.A conjecture is posed that the cited contribution covers all possible cases.A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λ n with induced components that are parallel paths of length > 1 is posed as well.