  A coordinate-space representation for a charged scalar particle propagator in
a constant magnetic field was obtained as a series over the Landau levels.
Using the recently developed modified Fock-Schwinger method, an intermediate
expression was constructed and symmetrized, thus, allowing for factorization of
the series terms into two factors. The first one, a sum of Bessel functions,
depends on time and $z$-coordinate, where the $z$-axis is chosen to be a
direction of the magnetic field, and has a structure similar to the propagator
of a free field. The second one, a product of a Laguerre polynomial and a
damping exponential, depends on $x,y$-coordinates, which form a plane
perpendicular to the direction of the magnetic field, and ensures the localized
propagation in the $x,y$-plane.
