A word that has many senses and motives put into.
Pouring alcohol, it’s altered from shuhai to sakazuki1. Cup = Holy Grail.
If written as sakadzuki2, it’s an inverted moon reflected in the cup. A fake moon.
Sakadzuki becomes the new moon, that means a dark night with no moon.
In this work, the moon frequently appears as a symbol of “miracles” or “Miyu.” The big full moon at the back in the scene in which it is revealed by Gil-kun that Miyu is a resident of a parallel world. The crescent moon in the teacup in the scene where Shirou and Kiritsugu have their last conversation at the porch. The waxing moon that barely remains faintly in Shirou’s Reality Marble. The moment this moon wanes into a new moon, Shirou’s wish has been granted.

Translator’s Notes
  1. ^ 酒杯 (shuhai), 盃 (sakazuki). Both words mean ‘sake cup’ or simply ‘cup’.
  2. ^ 朔月 (sakadzuki). It reads almost the same as 盃, but its meaning is ‘reverse moon’. As a matter of fact, the correct reading of 盃 would be ‘sakadzuki’, same as 朔月. The kana づ (dzu) can be replaced by ず (zu) to simplify the reading.
PRISMA material/petit: Encyclopedia of Prisma Illya MOVIE