  In a galaxy cluster, the evolution of spiral galaxies depends on their
cluster environment. Ram pressure due to the rapid motion of a spiral galaxy
within the hot intracluster medium removes the galaxy's interstellar medium
from the outer disk. Once the gas has left the disk, star formation stops. The
passive evolution of the stellar populations should be detectable in optical
spectroscopy and multi-wavelength photometry. The goal of our study is to
recover the stripping age of the Virgo spiral galaxy NGC 4388, i.e. the time
elapsed since the halt of star formation in the outer galactic disk using a
combined analysis of optical spectra and photometry. We performed VLT FORS2
long-slit spectroscopy of the inner star-forming and outer gas-free disk of NGC
4388. We developed a non-parametric inversion tool that allows us to
reconstruct the star formation history of a galaxy from spectroscopy and
photometry. The tool was tested on a series of mock data using Monte Carlo
simulations. The results from the non-parametric inversion were refined by
applying a parametric inversion method. The star formation history of the
unperturbed galactic disk is flat. The non-parametric method yields a rapid
decline of star formation < 200 Myr ago in the outer disk. The parametric
method is not able to distinguish between an instantaneous and a long-lasting
star formation truncation. The time since the star formation has dropped by a
factor of two from its pre-stripping value is 190 +- 30 Myr. We are able to
give a precise stripping age that is consistent with revised dynamical models.
