Summary: A set of positive integers \(A\) is called a \(B_h[g]\) set if there are at most \(g\) different sums of \(h\) elements from \(A\) with the same result. This definition has a generalization to abelian groups and the main problem related to this kind of sets is to find \(B_h[g]\) maximal sets, i.e., those with larger cardinality. We construct \(B_h[g]\) modular sets from \(B_h\) modular sets using homomorphisms and analyze the constructions of \(B_h\) sets by Bose and Chowla, Ruzsa, and Gómez and Trujillo look at for the suitable homomorphism that allows us to preserve the cardinal of these types of sets.