Did Agatha Christie quote 'the wheels of the grist mill grind slowly but grind exceedingly fine'?

ANSWERS.com [mills-of-the-gods-grind-slowly] reports: "This expression comes from ancient Greek, translated as "The mills of the gods grind slowly, but they grind small." In English it appeared in George Herbert's Jacula Prudentum (1640) as "God's mill grinds slow but sure."

It was referenced in a poem by Friedrich von Logau in 1694: "Gottes Mühlen mahlen langsam, mahlen aber trefflich klein / Ob aus Langmut er sich säumet, bringt mit Schärf' er alles ein" which was translated by Longfellow as: "Though the mills of God grind slowly, yet they grind exceeding small; Though with patience He stands waiting, with exactness grinds He all." "They Grind Exceedingly Small" was used as the title of a short story by Ben Ames Williams publishing in the Saturday Evening Post in 1919.

"The mill of God grinds slow but grinds exceeding(ly) small" is a verbatim quote from the English translation of the Avestan language hymn book of Zoroastrianism. (Hafiz 546)