  We explicitly describe the last stages of black hole evaporation in the
context of string theory : the combined study of Quantum Field Theory (QFT) and
String Theory (ST) in curved backgrounds allows us to go further in the
understanding of quantum gravity effects. The string ``analogue model''(or
thermo-dynamical approach) is a well suited framework for this purpose.The
results also apply to another physically relevant case: de Sitter background.
Semiclassical (QFT) and quantum gravity (String) phases or regimes are properly
determined (back reaction effects included). The Hawking-Gibbons temperature
${T_H}$ of the semiclassical regime becomes the intrinsic string temperature
${T_S}$ in the quantum gravity regime.The spectrum of black hole evaporation is
an incomplete gamma function of $(T_S - T_H)$: the early evaporation is thermal
(Hawking radiation), while at the end the black hole undergoes a phase
transition to a string state decaying (as string decay) into pure (non mixed)
particle states.Remarquably, explicit dynamical computations show that both
gravity regimes: semiclassical (QFT) and quantum (string), are dual of each
other, in the precise sense of the classical-quantum (de Broglie type) duality.
