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Given a countable group G and two subshifts X and Y over G, a continuous, shift-commuting map 
$\phi : X \to Y$ is called a homomorphism. Our main result states that if G is locally virtually nilpotent, X is aperiodic, and Y has the finite extension property, then there exists a homomorphism 
$\phi : X \to Y$. By combining this theorem with the main result of [1], we obtain that if the same conditions hold, and if additionally the topological entropy of X is less than the topological entropy of Y and Y has no global period, then X embeds into Y.
