Valuation rings of mixed characteristic as limits of complete intersection rings

We show that a mixed characteristic valuation ring with a value group $\mathrm{\Gamma }$, $\text{val}$ its valuation and a residue field of characteristic $p>0$, is a filtered colimit of complete intersection $\mathbf{Z}$-algebras if $\mathrm{\Gamma }\mathrm{/}\mathbf{Z}\text{val}(p)$ has no $p$-torsion and $V$ is Henselian.