The irregular local-system Lagrangian realization conjecture

Let $X$ be a complex manifold, let $\cM$ be a meromorphic connection with poles in $D$, and let $f$ be a $C^\infty$ function on $X\setminus D$ such that $\Lambda^f$ represents the irregular local system corresponding to $\cM$. Let $L_{\cM}$ be the graph of the derivative of $f$ in $T^*X$, and let $\Fuk_m(T^*X)$ be the modified Fukaya category from the preceding conjecture.

Irregular local-system realization conjecture. The Lagrangian $L_{\cM}$ defines an object of $\Fuk_m(T^*X)$ independent of the choice of $f$. The full subcategory of $\Fuk_m(T^*X)$ consisting of such objects is denoted by $\Fuk_{icnov}(T^*X)$.

This is the second ingredient of the proposed Fukaya-categorical construction of irregular perverse sheaves. The source explains that the choice of $f$ is only up to bounded modification and says that the construction should extend to arbitrary irregular local systems, but gives no proof.