  We explore the acceleration effect on the genuine tripartite nonlocality
(GTN) for one or two accelerated detector(s) coupled to the vacuum field with
initial mixed tripartite states. We show that the Hawking radiation degrades
the physically accessible GTN, which suffers from "sudden death" at certain
critical Hawking temperature. An novel phenomenon has been observed first time
that the Hawking effect can generate the physically inaccessible GTN for
fermion fields in curved spacetime, the "sudden birth" of the physically
inaccessible GTN. This result shows that the GTN can pass through the event
horizon of black hole for certain mixed initial states. We also derived
analytically the tradeoff relations of genuine tripartite entanglement (GTE)
and quantum coherence under the influence of Hawking effect.
