  We demonstrate within the quantum field theoretical framework that an
asymptotic particle falling into the black hole implants soft graviton hair on
the horizon, conforming with the classical proposal of Hawking, Perry and
Strominger. A key ingredient to this result is the construction of
gravitational Wilson line dressings of an infalling scalar field, carrying a
definite horizon supertranslation charge. It is shown that a typical
Schwarzschild state is degenerate, and can be labeled by different soft
supertranslation hairs parametrized for radial trajectories by the mass and
energy of the infalling particle and its asymptotic point of contact with the
horizon. The supertranslation zero modes are also obtained in terms of
zero-frequency graviton operators, and are shown to be the expected canonical
partners of the linearized horizon charge that enlarge the horizon Hilbert
space.
