Invertible bimodule categories over the representation category of a Hopf algebra

For any finite-dimensional Hopf algebra $H$ we construct a group homomorphism $\text{biga}(H)\to \text{BrPic}(\text{Rep}(H))$, from the group of equivalence classes of $H$-biGalois objects to the group of equivalence classes of invertible exact $\text{Rep}(H)$-bimodule categories. We discuss the injectivity of this map. We exemplify in the case $H=T_q$ is a Taft Hopf algebra and for this we classify all exact indecomposable $\text{Rep}(T_q)$-bimodule categories.