  On the basis of 16 years of spectroscopic observations of the four components
of the gravitationally lensed broad absorption line (BAL) quasar H1413+117,
covering the ultraviolet to visible rest-frame spectral range, we analyze the
spectral differences observed in the P Cygni-type line profiles and have used
the microlensing effect to derive new clues to the BAL profile formation. We
confirm that the spectral differences observed in component D can be attributed
to a microlensing effect lasting at least a decade. We show that microlensing
magnifies the continuum source in image D, leaving the emission line region
essentially unaffected. We interpret the differences seen in the absorption
profiles of component D as the result of an emission line superimposed onto a
nearly black absorption profile. We also find that the continuum source and a
part of the broad emission line region are likely de-magnified in component C,
while components A and B are not affected by microlensing. We show that
microlensing of the continuum source in component D has a chromatic dependence
compatible with the thermal continuum emission of a standard Shakura-Sunyaev
accretion disk. Using a simple decomposition method to separate the part of the
line profiles affected by microlensing and coming from a compact region from
the part unaffected by this effect and coming from a larger region, we
disentangle the true absorption line profiles from the true emission line
profiles. The extracted emission line profiles appear double-peaked, suggesting
that the emission is occulted by a strong absorber, narrower in velocity than
the full absorption profile, and emitting little by itself. We propose that the
outflow around H1413+117 is constituted by a high-velocity polar flow and a
denser, lower velocity disk seen nearly edge-on.
