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A strong \( k \)-edge-coloring of a graph \( G \) is an assignment of \( k \) colors to the edges of \( G \) in such a way that any two edges meeting at a common vertex, or being adjacent to the same edge of \( G \), are assigned different colors. The strong chromatic index of \( G \) is the smallest number \( k \) for which \( G \) has a strong \( k \)-edge-coloring. A Halin graph is a planar graph consisting of a tree with no vertex of degree two and a cycle connecting the leaves of the tree. A caterpillar is a tree such that the removal of the leaves becomes a path. In this paper, we show that the strong chromatic index of cubic Halin graph is at most 9. That is, every cubic Halin graph is edge-decomposable into at most 9 induced matchings. Also, we study the strong chromatic index of a cubic Halin graph whose characteristic tree is a caterpillar.