  According to the fossil-field hypothesis magnetic fields are remnants of the
previous stages of evolution. However, population synthesis calculations are
unable to reproduce the magnetic white dwarf (MWD) sample without binary
interaction or inclusion of a population of progenitor with unobservable
small-scale fields. One necessary ingredient in population synthesis is the
initial-to-final-mass relation (IFMR) which describes the mass-loss processes
during the stellar evolution. When white dwarfs are members of open clusters,
their evolutionary histories can be assessed through the use of cluster
properties. In this work, we assess the cluster membership by correlating the
proper-motion of MWDs with the cluster proper-motion and by analyzing the
candidates spectroscopically with our magnetic model spectra in order to
estimate the effective temperature and radii. We identified SDSS
J085523.87+164059.0 to be a proper-motion member of Praesepe. We also included
the data of the formerly identified cluster members NGC 6819-8, WD 0836+201 and
estimated the mass, cooling age and the progenitor masses of the three probable
MWD members of open clusters. According to our analysis, the newly identified
cluster member SDSS J085523.87+164059.0 is an ultra-massive MWD of mass 1.12
$\pm$ 0.11 Msolar. We increase the sample of MWDs with known progenitor masses
to ten, with the rest of the data coming from the common proper motion
binaries. Our investigations show that, when effects of the magnetic fields are
included in the diagnostics, the estimated properties of these cluster MWDs do
not show evidence for deviations from the IFMR. Furthermore, we estimate the
precision of the magnetic diagnostics which would be necessary to determine
quantitatively whether magnetism has any effect on the mass-loss.
