K1-injectivity of the Paschke dual algebra for certain simple C*-algebras

Let $B$ be a separable simple stable C*-algebra with strict comparison of positive elements and $T\left(B\right)$ having finite extreme boundary, and let $A$ be a simple unital separable nuclear C*-algebra. We prove that the Paschke dual algebra $A_B^d$ is $K_1$-injective. As a consequence, we obtain interesting KK-uniqueness theorems which generalize the Brown–Douglas–Fillmore essential codimension property.