A non-trivially non-trivial automorphism at an inaccessible cardinal

We show that, relative to the existence of an inaccessible cardinal, it is consistent that for an inaccessible cardinal $\kappa$, there is a non-trivial automorphism of $\mathcal{P}(\kappa )\mathrm{/}\mathrm{f}\mathrm{i}\mathrm{n}$ whose restriction to $\mathcal{P}(\beta )\mathrm{/}\mathrm{f}\mathrm{i}\mathrm{n}$ is induced by a bijection on $\beta$ for every $\beta <\kappa$. This answers questions posed by Larson–McKenney, Shelah–Steprāns, and Veličković.