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