Transfer-principle conservation conjecture for Shoenfield-normal formulas

Let $[?]([?])$ be a formula in the language of $[?]$, and suppose its Shoenfield interpretation has the form

$$[?]([?])^[?]\equiv\forallst [?] \, [?] \existsst [?] \, [?]([?], [?], [?]).$$

If $[?]$ is a collection of internal formulas and

$$[?] + \I + \HAC_\intern + \TPA + [?] \vdash [?]([?]),$$

then

$$[?] + [?] \vdash \forall [?]\exists [?] [?]([?], [?], [?]).$$

Transfer-principle conservation conjecture. Under these hypotheses, the displayed internal consequence follows. The claim is introduced as a consequence that would establish the preceding conjectured conservation result; its resolution is not given in the supplied text.