Finding two store typings that make the same store valid (lambda-calculus with references)
The store $\mu$ indicates the type of what is stored in the reference. If $\Sigma(\ell) = T$ then the expression $!\ell$ has the type $T$, and the expression $\ell$ has the type $\mathsf{Ref}(T)$.

If all you need is for $\lambda x:\mathsf{Unit}. (!\ell)(x)$ to be well-typed, then $\ell$ must be a reference to a function whose argument type is $\mathsf{Unit}$, with no constraint on the return type.