Question:
Shalom
Is there a source for the minhag to recite the entire sefer Devarim on the night of Hoshanah Rabah?
Answer:
Hello,
The source of reading Mishna Torah on the night of Hoshana Rabba, is based on kabbalah, see Pri Eitz Chaim Shar Hakavanos pg. 102. It is written that we specifically read Sefer Devarim because it contains many ideas which are the basics regarding Yiras Hashem and Ahavas Hashem. See Sources.
Sources:
ערוך השולחן אורח חיים סימן תרסד סעיף יא
וקורין משנה תורה מפני שבשם עיקר אהבת ד' ויראתו