Transporting pseudo-monad structure along a pseudo-natural equivalence

Question

Suppose that we have a pseudo-monad $\mathbb{T}$ (with underlying pseudo-functor $T$) on a $2$-category $\mathcal{K}$. Suppose also that there is a pseudo-natural equivalence between $T$ and another pseudo-functor $S$ on $\mathcal{K}$. Can we transport the pseudo-monad structure $\mathbb{T}$ on $T$ along this pseudo-natural equivalence to obtain a pseudo-monad structure on $S$, and if so, is there a result in the literature that attests to this?