Zilber's isomorphism conjecture for the complex exponential field

Let $\mathbb{C}_{\mathrm{exp}}$ denote the complex exponential field and let $\mathbb{B}_{\mathrm{exp}}$ denote Zilber's quasiminimal excellent exponential field constructed by the Hrushovski--Fraïssé amalgamation-with-predimension method. The axioms in question include the algebraic properties of $\mathbb{C}_{\mathrm{exp}}$, Schanuel's conjecture, Strong Exponential-Algebraic Closedness, and the countable closure property. Zilber's isomorphism conjecture. One has

$$\mathbb{C}_{\mathrm{exp}}\cong\mathbb{B}_{\mathrm{exp}}.$$

More precisely, $\mathbb{C}_{\mathrm{exp}}$ is a model of these axioms; equivalently, Schanuel's conjecture holds in $\mathbb{C}_{\mathrm{exp}}$ and $\mathbb{C}_{\mathrm{exp}}$ is Strongly Exponentially-Algebraically Closed. This is presented as a strengthening of Zilber's quasiminimality conjecture. The supplied text does not state that it has been resolved, so it remains open.