  We tackle the problem of constructing $R$-matrices for the category
$\mathcal{O}$ associated to the Borel subalgebra of an arbitrary untwisted
quantum loop algebra $U_q(\mathfrak{g})$. For this, we define an exact functor
$\mathcal{F}_q$ from the category $\mathcal{O}$ linked to
$U_{q^{-1}}(\mathfrak{g})$ to the one linked to $U_q(\mathfrak{g})$. This
functor $\mathcal{F}_q$ is compatible with tensor products, preserves
irreducibility and interchanges the subcategories $\mathcal{O}^+$ and
$\mathcal{O}^-$ of (D. Hernandez, B. Leclerc, Algebra Number Theory, 2016). We
construct $R$-matrices for $\mathcal{O}^+$ by applying $\mathcal{F}_q$ on the
braidings already found for $\mathcal{O}^-$ in (D. Hernandez, Rep. Theory,
2022). We also use the factorization of the latter intertwiners in terms of
stable maps to deduce an analogous factorization for our new braidings. We
finally obtain as byproducts new relations for the Grothendieck ring
$K_0(\mathcal{O})$ as well as a functorial interpretation of a remarkable ring
isomorphism $K_0(\mathcal{O}^+)\simeq K_0(\mathcal{O}^-)$ of
Hernandez--Leclerc.
