  Previously, we developed the technique of balayage of measures or charges and
($\delta$-)subharmonic functions of finite order onto an closed system of rays
$S$ with a vertex at zero on the complex plane $\mathbb C$. In this article, we
use only two kinds of balayage of measure and charge, as well as of subharmonic
functions of finite type under the order $1$ and their differences. First, it
is a classical balayage of the genus $q=0$ on a system of four closed rays:
positive and negative, and real and imaginary semi-axis $\mathbb R^+$,
$-\mathbb R^+$, $i\mathbb R^+$, $-i\mathbb R$. Second, it is two-sided balayage
of genus $q=1$ from the open right and left half-planes $\mathbb C_{{\rm rh}}$
and $\mathbb C_{{\rm lh}}$ onto the imaginary axis $i\mathbb R$. The classical
Malliavin-Rubel theorem gives necessary and sufficient conditions of the
existence of an entire function of exponential type (we write e.f.e.t.)
$f\not\equiv 0$, vanishing on the given positive sequence ${\sf Z}=\{{\sf
z}_k\}_{k\in \mathbb N}\subset \mathbb R^+$ and satisfying the constraint
$|f|\leq |g|$ on $i\mathbb R$, where $g$ is an e.f.e.t., vanishing on positive
sequence ${\sf W}=\{{\sf w}_k\}_{k\in \mathbb N}\subset \mathbb R^+$. A
combination of these special balayage processes of genus $q=0$ and $q=1$ allows
us to extend the Malliavin-Rubel theorem to arbitrary complex sequences ${\sf
Z}=\{{\sf z}_k\}_{k\in \mathbb N}\subset \mathbb C$ separated by a pair of
vertical angles from the imaginary axis $i\mathbb R$, with much more general
restrictions $\ln |f|\leq M$ on the imaginary axis $i\mathbb R$, where $M$ is
an subharmonic function of finite type under the order $1$.
