  Given a pseudomonad $\mathcal{T} $, we prove that a lax $\mathcal{T}
$-morphism between pseudoalgebras is a $\mathcal{T} $-pseudomorphism if and
only if there is a suitable (possibly non-canonical) invertible $\mathcal{T}
$-transformation. This result encompasses several results on
\textit{non-canonical isomorphisms}, including Lack's result on normal monoidal
functors between braided monoidal categories, since it is applicable in any
$2$-category of pseudoalgebras, such as the $2$-categories of monoidal
categories, cocomplete categories, pseudofunctors and so on.
