  The recently observed chirping signature in the light curves of Seyfert 1
galaxy SDSSJ1430$+$2303 could be explained by a late-inspiralling supermassive
binary black hole (SMBBH) system in the galactic center, which will merge in
the near future (or could have merged already). For the merging SMBBH scenario,
SDSSJ1430$+$2303 can be a source of nonlinear gravitational wave (GW) burst
with memory (BWM), which may provide a promising target for future pulsar
timing array (PTA) observations. In this work, we investigate the prospects for
detecting the BWM signal from SDSSJ1430$+$2303 by the International PTA (IPTA)
and FAST-PTA in the next $5$ years. We firstly propose strategies on searching
for this target signal, including the selection of millisecond pulsars (MSPs)
and the distribution of observation time. Then we simulate PTA observations
based on the proposed strategies and obtain the probability density functions
of the network signal-to-noise ratio and parameter-estimation errors of the BWM
signal, considering the uncertainties of parameters of the SMBBH and both white
and red noises of the selected MSPs. Our result shows that although IPTA can
marginally detect the BWM in $5$ years, FAST-PTA can detect it with
significantly higher confidence. Moreover, the archived IPTA data is important
in estimating the merger time of the SMBBH, when combined with the FAST-PTA
data. This work can serve as a guidance for future PTA observations and
multi-messenger studies on SDSSJ1430$+$2303 and similar systems.
