  Neutron star-helium white dwarf (NS+He WD) binaries are important
evolutionary products of close-orbit binary star systems. They are often
observed as millisecond pulsars and may continue evolving into ultra-compact
X-ray binaries (UCXBs) and continuous gravitational wave (GW) sources that will
be detected by space-borne GW observatories, such as LISA, TianQin and Taiji.
Nevertheless, the stability of NS+He WD binaries undergoing mass transfer is
not well studied and still under debate. In this paper, we model the evolution
of NS+He WD binaries with WD masses ranging from 0.17-0.45 $M_{\odot}$,
applying the detailed stellar evolution code mesa. Contrary to previous studies
based on hydrodynamics, we find that apparently all NS+He WD binaries undergo
stable mass transfer. We find for such UCXBs that the larger the WD mass, the
larger the maximum mass-transfer rate and the smaller the minimum orbital
period during their evolution. Finally, we demonstrate numerically and
analytically that there is a tight correlation between WD mass and GW frequency
for UCXBs, independent of NS mass.
