The privilege of wearing letters is not "inherited" in any group - unless they have a cute shirt that says "XYZ Baby" and those are for, well, babies.
If your son does give her that privilege - and it would come through him, not her parents - he needs to clear it with his chapter first and as moe.ron said, who and why can wear letters (outside of members) depends on the chapter.
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It is all 33girl's fault. ~DrPhil
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