  Evolutionary tracks of stars with masses on the main sequence $0.84M_\odot\le
M_\textrm{ZAMS}\le 0.95M_\odot$ and initial metal abundances $Z=0.006$ and
$Z=0.01$ were computed under various assumptions about the mass loss rate at
the red giant stage as well as at the AGB and the post--AGB stages. Among 160
evolutionary sequences we selected nearly 30 sequences where the final thermal
flash of the helium shell source occurs in the early post--AGB stage when the
ratio of the hydrogen envelope mass to the stellar mass ranges from 0.01 to
0.08. Selected evolutionary sequences were used for calculation of initial and
inner boundary conditions used in solution of the equations of radiation
hydrodynamics and turbulent convection describing evolution of stellar
pulsations after the helium flash. Among about three dozen hydrodynamic models
we found the three ones demonstrating almost eightfold increase of the
pulsation period observed in V725 Sgr during the last century as well as the
gradual transformation of fairly regular pulsations with period $\Pi\approx 12$
day to semi--regular non--linear oscillations with period $80~\textrm{day}
\lesssim\Pi\lesssim 90~\textrm{day}$. We conclude that the anomalous growth of
the pulsation period in V725 Sgr is due to the final thermal flash of the
helium shell source that occurred in the early post--AGB star with mass
$M\approx 0.53M_\odot$ and the mass of the hydrogen envelope ranging from
$0.013M_\odot$ to $0.019M_\odot$.
