  Despite much effort for over the two decades, the paring symmetry of a
Sr$_2$RuO$_4$ superconductor has been still unclear. In this Rapid
Communication, motivated by the recent rapid progress in fabrication techniques
for Sr$_2$RuO$_4$ thin-films, we propose a promising strategy for identifying
the spin-triplet superconductivity in the thin-film geometry by employing an
antisymmetric spin-orbit coupling potential and a Zeeman potential due to an
external magnetic field. We demonstrate that a spin-triplet superconducting
thin-film undergoes a phase transition from a helical state to a chiral state
by increasing the applied magnetic field. This phase transition is accompanied
by a drastic change in the property of surface Andreev bound states. As a
consequence, the helical-chiral phase transition, which is unique to the
spin-triplet superconductors, can be detected through a sudden change in a
tunneling conductance spectrum of a normal-metal/superconductor junction.
Importantly, our proposal is constructed by combining fundamental and rigid
concepts regarding physics of spin-triplet superconductivity.
