Let $\mathfrak{g}$ be a finite-dimensional (complex) semisimple Lie algebra. Then we denote the BGG category for $\mathfrak{g}$ by $\mathcal{O}$ as usual. It is well-known that $\mathcal{O}$ as well as its (indecomposable) blocks are highest weight categories in the sense of the paper "Finite-dimensional algebras and highest weight categories" by Cline, Parshall and Scott.
$\text{My question:}$ Is there any example giving an equivalence $F$ between blocks which does not preserve highest weight structure? That is, $F$ does not send standard objects to standard objects. Thanks!