Bowen's f-invariant entropy addition conjecture

Let $r\in\mathbb N$, and let $A$, $B$, and $C$ be $Z(F_r)$-modules in an exact sequence

$$0\longrightarrow A\longrightarrow B\longrightarrow C\longrightarrow 0.$$

Suppose that the actions of $F_r$ on $(\widehat{A},\lambda_{\widehat{A}})$, $(\widehat{B},\lambda_{\widehat{B}})$, and $(\widehat{C},\lambda_{\widehat{C}})$ all have finite generating partitions. Bowen's f-invariant entropy addition conjecture. Then

$$f_{\lambda_{\widehat{B}}}(\widehat{B},F_r)=f_{\lambda_{\widehat{A}}}(\widehat{A},F_r)+f_{\lambda_{\widehat{C}}}(\widehat{C},F_r).$$

This is the proposed opposite behavior to the preceding non-additivity conjecture: under the stated finite-generation hypotheses, Bowen's $f$-invariant entropy should satisfy an addition formula. The source further suggests an analogous statement for random sofic entropy.