Universality of the central extension of the annulus semigroup

Let $\operatorname{Ann}$ be the semigroup of annuli, and consider the central extension

$$0\to\mathbb{C}\times\mathbb{Z}\to\operatorname{A\widetilde{\!\!\phantom{i}n\phantom{i}\!\!}n}\to\operatorname{Ann}\to0.$$

Universality conjecture. This central extension is a universal central extension. The claim concerns universality in the category of central extensions of the annulus semigroup. The source does not state a resolution.