Proof.
By [ES22, Thm. 2.2.9], for any additive, idempotent complete \(\infty\)-category \(\mathcal A\), the \(\infty\)-category \(\mathcal A^{\mathrm{fin}}\) is uniquely characterized by being a stable, idempotent-complete \(\infty\)-category with bounded weight structure with weight heart \(\mathcal A\). Since for an ordinary, additive, idempotent-complete \(1\)-category \(\mathcal A\), the \(\infty\)-category \({\mathbf K}^b(\mathcal A)\) is a stable, idempotent-complete \(\infty\)-category with weight structure and weight heart \(\mathcal A\), see proposition 3.4.2, example 3.4.8. The result follows. ◻