  We obtain one family of dynamic solutions in the Einstein-Maxwell-scalar(EMS)
theory. Our solutions could describe the evolving charged black(white) hole or
wormhole and its transition, including the case of black bounce/wormhole
transition. We compare different wormhole throat definitions and suggest that
the usage of trapping horizons is the most suitable choice for tracking the
evolution of the dynamic black(white) hole and wormhole, and their conversion
in a unified framework. Then we research several evolving processes in the
appropriate parameters region, including the charge, the initial condition for
the scalar hair, and parameters in our EMS Lagrangian. The results show that
the appearance of a degenerate marginal trapped surface is the crucial event
for the conversion or transition, particularly in these cases: i) when the
evolving wormhole converts to a black hole, the surface emerges and splits into
two trapping horizons; ii) if the metric would become a black hole but finally
fails, two trapping horizons combine as the surface and then vanish; iii) if
the black bounce/wormhole transition happens, one single trapping horizon
changes its type.
