  We present a microscopic theory of the superconducting proximity effect in a
semiconducting thin film with spin-orbit interaction ($N_{SO}$) in an external
magnetic field. We demonstrate that an effective 1D Hamiltonian which describes
induced superconductivity in $N_{SO}$ in contact with a usual $s$-wave
superconductor possesses not only spin-singlet induced superconducting order
parameter term, as commonly adopted, but spin triplet order parameter term
also. Using this new effective Hamiltonian we confirm previous results for a
normal current across contacts of $N_{SO}$ with a normal metal and for a
Josephson current with the same $N_{SO}$ with induced superconductivity,
obtained previously in the framework of the phenomenological Hamiltonian
without spin-triplet terms. However, a calculated current-phase relation across
the transparent contact between $N_{SO}$ with induced superconductivity in
magnetic field and usual $s$-wave superconductor differs significantly from
previous results. We suggest the experiment which can confirm our theoretical
predictions.
