  We explore the process of orbital angular momentum (OAM) transfer from a
twisted light beam to an electron in atomic ionization within the first Born
approximation. The characteristics of the ejected electron are studied
regardless of the detection scheme. We find that the outgoing electron
possesses a definite projection of OAM when a single atom is located on the
propagation axis of the photon, whereas the size of the electron wave packet is
solely determined by the energy of the photon rather than by its transverse
coherence length. Shifting the position of the atom yields a finite dispersion
of the electron OAM. We also study a more experimentally feasible scenario -- a
localized finite-sized atomic target -- and develop representative approaches
to describing coherent and incoherent regimes of photoionization.
