Let g be a symmetrizable Kac-Moody Lie algebra, and let Vgˆ,ħℓ, Lgˆ,ħℓ be the quantum affine vertex algebras constructed in [11]. For any complex numbers ℓ and ℓ′, we present an ħ-adic quantum vertex algebra homomorphism Δ from Vgˆ,ħℓ+ℓ′ to the twisted tensor product ħ-adic quantum vertex algebra Vgˆ,ħℓ⊗ˆVgˆ,ħℓ′. In addition, if both ℓ and ℓ′ are positive integers, we show that Δ induces an ħ-adic quantum vertex algebra homomorphism from Lgˆ,ħℓ+ℓ′ to the twisted tensor product ħ-adic quantum vertex algebra Lgˆ,ħℓ⊗ˆLgˆ,ħℓ′. Moreover, we prove the coassociativity of Δ.