$\mathrm{ı}$Hall algebras of weighted projective lines and quantum symmetric pairs II: injectivity

We show that the morphism $\mathrm{\Omega }$ from the $\mathrm{ı}$quantum loop algebra ${}^{\mathtt{\text{Dr}}}\tilde{\mathbf{U}}(L\mathfrak{g})$ of split type to the $\mathrm{ı}$Hall algebra of the weighted projective line is injective if $\mathfrak{g}$ is of finite or affine type. As a byproduct, we use the whole $\mathrm{ı}$Hall algebra of the cyclic quiver $C_n$ to realise the $\mathrm{ı}$quantum loop algebra of affine ${\mathfrak{g}\mathfrak{l}}_n$.