AbstractWe study random walks on the lampshuffler group $$\textrm{FSym}(H)\rtimes H$$ FSym ( H ) ⋊ H , where H is a finitely generated group and $$\textrm{FSym}(H)$$ FSym ( H ) is the group of finitary permutations of H. We show that for any step distribution $$\mu $$ μ with a finite first moment that induces a transient random walk on H, the permutation coordinate of the random walk almost surely stabilizes pointwise. Our main result states that for $$H=\mathbb {Z}$$ H = Z , the above convergence completely describes the Poisson boundary of the random walk $$(\textrm{FSym}(\mathbb {Z})\rtimes \mathbb {Z},\mu )$$ ( FSym ( Z ) ⋊ Z , μ ) .