Coincidence conjecture for the two Eisenstein-series isomorphisms

Let $G$ be a reductive group, let $\cB$ be a Borel subgroup of its Langlands dual group, and let $E_\cT$ be a regular $\cT$-local system. For a dominant coweight $\cla$ and a component indexed by $\cmu$, the source constructs two isomorphisms between the same objects, including an isomorphism

$$\imath^!_\cla(\IC_{\BunBb^\cmu})\simeq \fU(\cn_X)^\cla\boxtimes \IC_{\Bun_B^\{\cmu+\cla\}}.$$

Coincidence conjecture. The isomorphisms supplied by Proposition 'IC calculation' and Theorem 'FFKM thm' (1) coincide. This is a compatibility assertion internal to the proof of the Eisenstein-series description, rather than a broad independent conjecture. The source gives no resolution evidence beyond its placement in a conjecture environment.