The German equivalent is more or less "Gott mit uns" which was first used by Frederick I (also of Brandenburg-Prussia) in 1701.
The motto dates back to the early Norman conquests, but Henry III was the first to bring the phrase to prominence.
I would expect it came to the Hohenzollerns via their early grants from Henry V and VI, likely starting around the time of Conrad I, via the Franconian Nuremberg branch.
Brandenburg was brought into the House by the Franconian Hohenzollerns ca. 1415 with Frederick VI (Frederick I, Margrave-Elector of Brandenburg-Prussia)
That's all speculation on my part. The use is extremely unusual, I agree, without historical precedent and not repeated elsewhere before or after until it was adopted by the Hanoverians along with another well-known Norman French phrase - "Honi soit qui mal y pense" - and the German "Ich dien" (I serve.)
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