  Context. Globular clusters host stars with chemical peculiarities. The
associated helium enrichment is expected to affect the evolution of stars, in
general, and of low-mass stars, and in particular the progenitors of white
dwarfs (WDs). Aims. We investigate the effects of different initial helium
contents on the properties of white dwarfs such as their masses, compositions,
and the time since their formation. Results. In a globular cluster at a given
age, the He enrichment implies lower initial masses for stars at a given phase.
Thus it leads to a decrease of the masses of white dwarfs reaching the cooling
sequence. In addition the He enrichment increases the total mass and number of
white dwarfs and eventually allows the presence of He white dwarf from single
progenitors. Conclusions. The low He enrichment determined in most globular
clusters with different methods results in negligible effects on the white
dwarf properties. However, in the few globular clusters that display a high He
enrichment, this may significantly affect the characteristics of the white
dwarfs. In NGC 2808 and {\omega} Centauri the high He enrichment even leads to
the formation of He white dwarfs from single He-rich progenitors. Therefore
investigating the white dwarf mass domain in globular clusters with a high He
enrichment would provide an additional indirect way to measure and constrain
the He enrichment degree.
