  In this paper we study Devinatz's moment problem: to find a non-negative
Borel measure $\mu$ in a strip $\Pi = \{(x,\phi):\ x\in \mathbb{R},\ -\pi\leq
\phi < \pi\},$ such that $\int_\Pi x^m e^{in\phi} d\mu = s_{m,n}$, $m\in
\mathbb{Z}_+$, $n\in \mathbb{Z}$, where $\{s_{m,n}\}_{m\in \mathbb{Z}_+, n\in
\mathbb{Z}}$ is a given sequence of complex numbers. We present a new proof of
the Devinatz solvability criterion for this moment problem. We obtained a
parameterization of all solutions of Devinatz's moment problem. We used an
abstract operator approach and results of Godi\v{c}, Lucenko and Shtraus.
