  The Coulomb interaction generally limits the quantum propagation of
electrons. However, it can also provide a mechanism to transfer their quantum
state over larger distances. Here, we demonstrate such a form of teleportation,
across a metallic island within which the electrons are trapped much longer
than their quantum lifetime. This effect originates from the low temperature
freezing of the island's charge $Q$ which, in the presence of a single
connected electronic channel, enforces a one-to-one correspondence between
incoming and outgoing electrons. Such high-fidelity quantum state imprinting is
established between well-separated injection and emission locations, through
two-path interferences in the integer quantum Hall regime. The added electron
quantum phase of $2\pi Q/e$ can allow for strong and decoherence-free
entanglement of propagating electrons, and notably of flying qubits.
