  SDSS J080434.20+510349.2 is the WZ type binary that displayed rare outburst
in 2006 (Pavlenko et al., 2007). During the long-lasting tail of the late stage
of the outburst binary shown the two-humped or four-humped profile of the
orbital light modulation. The amplitude of orbital light curve decreased while
the mean brightness decreased, more over that occurred $\sim$ 10 times faster
during the fast outburst decline in respect to the late quiet state of slow
outburst fading. There were no white dwarf pulsations detected neither 1 - 1.5
months prior to the outburst nor in 1.5 - 2 months after the 2006 outburst in
this system. However the strong non-radial pulsations with period 12.6 minutes
and mean amplitude of 0.05^m were first detected in V band with 2.6-m Shajn
mirror telescope of the Crimean astrophysical observatory in ~ 8 months after
the outburst. The evolution of pulsations over two years in 2006 - 2008 is
considered. It is supposed that pulsations first appeared when the cooling
white dwarf (after the outburst) entered the instability strip although the
possibility of temporary lack of pulsations at some occasions also could not be
excluded.
