  The M dwarf GJ 436 hosts a transiting warm Neptune known to experience
atmospheric escape. Previous observations revealed the presence of a giant
hydrogen exosphere transiting the star for more than 5 h, and absorbing up to
56% of the flux in the blue wing of the stellar Lyman-{\alpha} line of neutral
hydrogen (H i Ly{\alpha}). The unexpected size of this comet-like exosphere
prevented observing the full transit of its tail. In this Letter, we present
new Ly{\alpha} observations of GJ 436 obtained with the Space Telescope Imaging
Spectrograph (STIS) instrument onboard the Hubble Space Telescope. The
stability of the Ly{\alpha} line over six years allowed us to combine these new
observations with archival data sets, substantially expanding the coverage of
the exospheric transit. Hydrogen atoms in the tail of the exospheric cloud keep
occulting the star for 10-25 h after the transit of the planet, remarkably
confirming a previous prediction based on 3D numerical simulations with the
EVaporating Exoplanet code (EVE). This result strengthens the interpretation
that the exosphere of GJ 436b is shaped by both radiative braking and charge
exchanges with the stellar wind. We further report flux decreases of 15 +/- 2%
and 47 +/- 10% in the red wing of the Ly{\alpha} line and in the line of
ionised silicon (Si iii). Despite some temporal variability possibly linked
with stellar activity, these two signals occur during the exospheric transit
and could be of planetary origin. Follow-up observations will be required to
assess the possibility that the redshifted Ly{\alpha} and Si iii absorption
signatures arise from interactions between the exospheric flow and the magnetic
field of the star.
