  The vertex function ($\Gamma$) within the Green's function formalism
encapsulates information about all higher-order electron-electron interaction
beyond those mediated by density fluctuations. Herein, we present an efficient
approach that embeds vertex corrections in the one-shot $GW$ correlation
self-energy for isolated and periodic systems. The vertex-corrected self-energy
is constructed through the proposed separation-propagation-recombination
procedure: the electronic Hilbert space is separated into an active space and
its orthogonal complement denoted as the "rest"; the active component is
propagated by a space-specific effective Hamiltonian different from the rest.
The vertex corrections are introduced by a rescaled time-dependent non-local
exchange interaction. The direct $\Gamma$ correction to the self-energy is
further updated by adjusting the rescaling factor in a self-consistent
post-processing circle. Our embedding method is tested mainly on donor-acceptor
charge-transfer systems. The embedded vertex effects consistently and
significantly correct the quasiparticle energies of the gap-edge states. The
fundamental gap is generally improved by 1-3 eV upon the one-shot $GW$
approximation. Furthermore, we provide an outlook for applications of
(embedded) vertex corrections in calculations of extended solids.
