Does a left-handed man have to start wearing his clothes from the left side - because his important hand is left, or from the right side - because this is an important hand for most of people?
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According to the Deberziner Zatzal in Shaalos UTshuvos Beer Moshe - Kuntururs Itur Yad - from the right side like all others.
Like everything else that is done for Kabbalistic reasons, a lefty does the same as a righty.