From $τ$-tilting to $τ_2$-tilting via splitting tilting triples

Let $(A,T,B)$ be a splitting tilting triple. We provide a construction of $τ_2$-tilting $B$-modules from $τ$-tilting $A$-modules. On the other hand, if $A$ is hereditary, by considering the mutation of a certain two-term silting complex of $A$ and its image under the derived equivalence $\mathbf{R}{