  We propose to embed the General NMSSM (Next-to-Minimal Supersymmetric
Standard Model) into the deflected AMSB (Anomaly Mediated Supersymmetry
Breaking) mechanism with Yukawa/gauge deflection contributions. After
integrating out the heavy messenger fields, the analytical expressions of the
relevant soft SUSY breaking spectrum for General NMSSM at the messenger scale
can be calculated. We find that successful EWSB (Electroweak Symmetry Breaking)
and realistic low energy NMSSM spectrum can be obtained in some parameter
regions. In addition, we find that the muon $g-2$ anomaly and electron $g-2$
anomaly (for positive central value electron $g-2$ experimental data) can be
jointly explained to $1\sigma$ and $2\sigma$ range, respectively. The $Z_3$
invariant NMSSM, which corresponds to $\xi_F=0$ in our case, can also jointly
explain the muon and electron anomaly to $1\sigma$ and $2\sigma$ range,
respectively.
