  Let $R$ be a discrete valuation domain with field of fractions $Q$ and
maximal ideal generated by $\pi$. Let $\Lambda$ be an $R$-order such that
$Q\Lambda$ is a separable $Q$-algebra. Maranda showed that there exists
$k\in\mathbb{N}$ such that for all $\Lambda$-lattices $L$ and $M$, if
$L/L\pi^k\simeq M/M\pi^k$ then $L\simeq M$. Moreover, if $R$ is complete and
$L$ is an indecomposable $\Lambda$-lattice, then $L/L\pi^k$ is also
indecomposable. We extend Maranda's theorem to the class of $R$-reduced
$R$-torsion-free pure-injective $\Lambda$-modules.
  As an application of this extension, we show that if $\Lambda$ is an order
over a Dedekind domain $R$ with field of fractions $Q$ such that $Q\Lambda$ is
separable then the lattice of open subsets of the $R$-torsion-free part of the
right Ziegler spectrum of $\Lambda$ is isomorphic to the lattice of open
subsets of the $R$-torsion-free part of the left Ziegler spectrum of $\Lambda$.
  Finally, with $k$ as in Maranda's theorem, we show that if $M$ is
$R$-torsion-free and $H(M)$ is the pure-injective hull of $M$ then
$H(M)/H(M)\pi^k$ is the pure-injective hull of $M/M\pi^k$. We use this result
to give a characterisation of $R$-torsion-free pure-injective $\Lambda$-modules
and describe the pure-injective hulls of certain $R$-torsion-free
$\Lambda$-modules.
