There is a slight difference. Phi Mu has a recommendation letter that you print out and give to the chapter from any Phi Mu alumna. At schools such as Auburn it is also good to have a personal written letter emphasizing your strengths from a alumna of that chapter. The general letter works best at a school but in the competative recruitment at Auburn, Florida, Ole Miss a person letter from an alumna helps. Even in the general Phi Mu form it ask the relationship between you so any recs should come from someone you know well.
So you're a Phi Mu?
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AOII
One Motto, One Badge, One Bond and Singleness of Heart!