  Given a simple Lie algebra $\mathfrak{g}$ and an element
$\mu\in\mathfrak{g}^*$, the corresponding shift of argument subalgebra of
$\text{S}(\mathfrak{g})$ is Poisson commutative. In the case where $\mu$ is
regular, this subalgebra is known to admit a quantization, that is, it can be
lifted to a commutative subalgebra of $\text{U}(\mathfrak{g})$. We show that if
$\mathfrak{g}$ is of type $A$, then this property extends to arbitrary $\mu$,
thus proving a conjecture of Feigin, Frenkel and Toledano Laredo. The proof
relies on an explicit construction of generators of the center of the affine
vertex algebra at the critical level.
