Tight closure/localization/geometric deformation over one dimensional domain/Fakt/Beweis

By localization, there exists  $h\in D$,   $h\ne 0$,  such that  $hf\in I^{\ast }\text{ in }R$. 

By persistence of tight closure (under a ring homomorphism) we get

$hf\in I^{\ast }\text{ in }{R}_{\kappa (𝔭)}.$

The element $h$ does not belong to $𝔭$ for almost all $𝔭$, so $h$ is a unit in $R_{\kappa (𝔭)}$ and hence

$f\in I^{\ast }\text{ in }{R}_{\kappa (𝔭)}$

for almost all $𝔭$.