  Let $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ be the modified quantum affine
$\frak{sl}_n$ and let ${\bf U}(\widehat{\frak{sl}}_N)^+$ be the positive part
of quantum affine $\frak{sl}_N$. Let $\dot{\mathbf{B}}(n)$ be the canonical
basis of $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ and let
$\mathbf{B}(N)^{\mathrm{ap}}$ be the canonical basis of ${\bf
U}(\widehat{\frak{sl}}_N)^+$. It is proved in \cite{FS} that each structure
constant for the multiplication with respect to $\dot{\mathbf{B}}(n)$ coincide
with a certain structure constant for the multiplication with respect to
$\mathbf{B}(N)^{\mathrm{ap}}$ for $n<N$. In this paper we use the theory of
affine quantum Schur algebras to prove that the structure constants for the
comultiplication with respect to $\dot{\mathbf{B}}(n)$ are determined by the
structure constants for the comultiplication with respect to
$\mathbf{B}(N)^{\mathrm{ap}}$ for $n<N$. In particular, the positivity property
for the comultiplication of $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ follows
from the positivity property for the comultiplication of ${\bf
U}(\widehat{\frak{sl}}_N)^+$.
