  Coupling to the environment typically suppresses quantum properties of
physical systems via decoherence mechanisms. This is one of the main obstacles
in practical implementations of quantum protocols. In this work we show how
decoherence effects can be reversed/suppressed during quantum teleportation in
a network scenario. Treating the environment quantumly, we show that under a
general pure dephasing coupling, performing a second teleportation step can
probabilistically reverse the decoherence effects if certain commutativity
conditions hold. This effect is purely quantum and most pronounced for qubit
systems, where in 25 % of instances the decoherence can be reversed completely.
As an example, we show the effect in a physical model of a qubit register
coupled to a bosonic bath. We also analyze general $d$-dimensional systems,
identifying all instances of decoherence suppression. Our results are
proof-of-concept but we believe will be relevant for the emerging field of
quantum networks as teleportation is the key building block of network
protocols.
