  The (full) extended plus closure was developed as a replacement for tight
closure in mixed characteristic rings. Here it is shown by adapting Andr\'{e}'s
perfectoid algebra techniques that, for complete local rings that have F-finite
residue fields, this closure has the colon-capturing property. In fact, more
generally, if $R$ is a (possibly ramified) complete regular local ring of mixed
characteristic that have F-finite residue fields, $I$ and $J$ are ideals of
$R$, and the local domain $S$ is a finite $R$-module, then $(IS:J)\subseteq
(I:J)S^{epf}$. A consequence is that all ideals in regular local rings are
closed, a fact which implies the validity of the direct summand conjecture and
the Brian\c{c}on-Skoda theorem in mixed characteristic.
