Infinite generalizations of theorems in finite combinatorics were initiated by Erdős due to his famous Erdős-Menger conjecture (now known as the Aharoni-Berger theorem) that extends Menger's theorem to infinite graphs in a structural way. We prove a generalization of this manner of the classical result about packing edge-disjoint $ T $-paths in an ``inner Eulerian'' setting obtained by Lovász and Cherkassky independently in the '70s.