  Optical excitation of stripe-ordered La$_{2-x}$Ba$_x$CuO$_4$ has been shown
to transiently enhance superconducting tunneling between the CuO$_2$ planes.
This effect was revealed by a blue-shift, or by the appearance of a Josephson
Plasma Resonance in the terahertz-frequency optical properties. Here, we show
that this photo-induced state can be strengthened by the application of high
external magnetic fields oriented along the c-axis. For a 7-Tesla field, we
observe up to a ten-fold enhancement in the transient interlayer phase
correlation length, accompanied by a two-fold increase in the relaxation time
of the photo-induced state. These observations are highly surprising, since
static magnetic fields suppress interlayer Josephson tunneling and stabilize
stripe order at equilibrium. We interpret our data as an indication that
optically-enhanced interlayer coupling in La$_{2-x}$Ba$_x$CuO$_4$ does not
originate from a simple optical melting of stripes, as previously hypothesized.
Rather, we speculate that the photo-induced state may emerge from activated
tunneling between optically-excited stripes in adjacent planes.
