  The aim of the present work is to investigate a non-minimally coupled scalar
field model through the Noether symmetry approach, with the radiation, matter
and cosmological constant eras being analyzed. The Noether symmetry condition
allows a conformal coupling and by means of a change of coordinates in the
configuration space the field equations can be reduced to a single equation,
which is of the form of the Friedmann equation for the $\Lambda$CDM model. In
this way, it is formally shown that the dynamical system can furnish solutions
with the same form as those of the $\Lambda$CDM model, although the theory here
considered is physically different from the former. The conserved quantity
associated with the Noether symmetry can be related to the kinetic term of the
scalar field and could constrain the possible deviations of the model from the
$\Lambda$CDM picture. Observational constraints on the variation of the
gravitational constant can be imposed on the model through the initial
condition of the scalar field.
