Splicing positroid varieties

We construct an explicit isomorphism between an open subset in the open positroid variety ${\mathrm{\Pi }}_{k,n}^{\circ }$ in the Grassmannian $\mathrm{G}\mathrm{r}(k,n)$ and the product of two open positroid varieties ${\mathrm{\Pi }}_{k,n-a+1}^{\circ }\times {\mathrm{\Pi }}_{k,a+k-1}^{\circ }$. In the respective cluster structures, this isomorphism is given by freezing a certain subset of cluster variables and applying a cluster quasi-equivalence.