  Binary systems made by a low-mass CO WD and a He-donor represent possible
progenitors of explosive events via He-detonation, producing low-luminosity
thermonuclear Supernovae with a peculiar nucleosynthetis. Recently, the binary
system PTF J223857.11+743015.1 has been suggested as one. We investigate the
evolution of the PTF J223857.11+743015.1 system, composed by a 0.75Msun CO WD
and a 0.390Msun subdwarf, capped by a thin H-rich layer, considering rotation
of the WD component. We compute the evolution of two stars simultaneously,
accounting for the possible evolution of the orbital parameters, as determined
by mass transfer between components and by mass ejection from the system during
RLOF episodes. We consider that the WD gains angular momentum due to accretion
and we follow the evolution of the angular velocity profile as due to angular
momentum transport via convection and rotation-induced instabilities. As the
donor H-rich envelope is transferred, the WD experiences recurrent very strong
H-flashes triggering RLOF episodes during which the entire accreted matter is
lost from the system. Due to mixing of chemicals by rotation-induced
instabilities during the accretion phase, H-flashes occur inside the original
WD. Hence, pulse-by pulse, the accretor mass is reduced down to 0.7453Msun.
When He-rich matter is transferred, He-detonation does not occur in the
rotating WD, which undergoes 6 very strong He-flashes and subsequent RLOF
episodes. Also in this case, due to rotation-induced mixing of the accreted
layers with the underlying core, the WD is eroded. Finally, when the mass
transfer rate from the donor decreases, a massive He-buffer is piled-up onto
the accretor which ends its life as a cooling WD. The binary system PTF
J2238+743015.1 as all those binaries having similar components masses and
orbital parameters are not good candidates as thermonuclear explosions
progenitors.
