Any friend of
any friend of (someone's) (is a friend of mine)
If we share a mutual friend, then we can be friends too. Oh, you know Henry too? Well, any friend of Henry's is a friend of mine! Oh sure, you can bring Ellen to the party. Any friend of yours.
Any friend of someone('s) (is a friend of mine).
Cliché. I am always pleased to meet a friend of someone I know. (A pleasant response when meeting or being introduced to a friend of a friend.) Fred: Well, nice to meet you, Tom. Any friend of my brother is a friend of mine. Tom: Thanks, Fred. Nice to meet you too. John: Thank you so much for helping me find Sue's address. Sally: You're welcome. Any friend of Sue's.