  Previous studies have shown that the Hawking effect always destroys quantum
correlations and the fidelity of quantum teleportation in the Schwarzschild
black hole. Here, we investigate the fidelity of quantum teleportation of Dirac
fields between users in Schwarzschild spacetime. We find that, with the
increase of the Hawking temperature, the fidelity of quantum teleportation can
monotonically increase, monotonically decrease, or non-monotonically increase,
depending on the choice of the initial state, which means that the Hawking
effect can create net fidelity of quantum teleportation. This striking result
banishes the extended belief that the Hawking effect of the black hole can only
destroy the fidelity of quantum teleportation. We also find that quantum
steering cannot fully guarantee the fidelity of quantum teleportation in
Schwarzschild spacetime. This new unexpected source may provide a new idea for
the experimental evidence of the Hawking effect.
