  It has been shown in [Yang-Yu 2019] that general large solutions to the
Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space
$\mathbb{R}^{1+3}$ decay like linear solutions. One hence can define the
associated radiation field on the future null infinity as the limit of
$(r\underline{\alpha}, r\phi)$ along the out going null geodesics. In this
paper, we show the existence of a global solution to the MKG system which
scatters to any given sufficiently localized radiation field with arbitrarily
large size and total charge. The result follows by studying the characteristic
initial value problem for the MKG system with general large data by using gauge
invariant vector field method. We in particular extend the small data result of
He in \cite{MR4299134} to a class of general large data.
