  Stellar evolution calculations to the stage of the cooling white dwarf were
done for population~I stars with masses on the main sequence $1M_\odot\le
M_0\le 1.5M_\odot$. The final helium flash LTP is shown to occur in post--AGB
stars with initial masses $1.3M_\odot\le M_0\le 1.32M_\odot$ for the
overshooting parameter $f=0.016$. In the case of more effective overshooting
($f=0.018$) the final helium flash occurs at initial masses $1.28M_\odot\le
M_0\le 1.3M_\odot$. Fivefold variations of the parameter responsible for the
mass loss rate during the post--AGB stage do not affect occurrence of the final
helium flash but lead to perceptible changes of the evolutionary time. Selected
models of two evolutionary sequences with initial mass $M_0 = 1.3M_\odot$
computed with overshooting parameters $f=0.016$ and $f=0.018$ were used as
initial conditions in solution of the equations of hydrodynamics describing
radial oscillations of stars on the stage of the final helium flash at
effective temperatures less than $10^4$ K. The maximum pulsation period
$\Pi=117$ day determined for the evolutionary sequence $M_0=1.3M_\odot$,
$f=0.016$ is in a good agreement with observational estimates of the period of
FG Sge. The mass, the radius and the effective temperature of the star are
$M=0.565M_\odot$, $R=126R_\odot$ and $T_\mathrm{eff}=4445$ K, respectively. At
the same time the average period change rate of FG Sge from 1960 to 1990 is
nearly three time larger than its theoretical estimate.
