I would say "She is Antonio's friend" But the other way(s) are fine too. I'm not sure exactly would be wrong with "a friend of Antonio" It may be a regionalism but I hear it a lot. For example "A friend of John is a friend of mine" "A friend of John's is a friend of mine" Is probably OK but it does not sound quite right to me.
The correct form is definitely "a friend of John's", although of course you will always hear people say it the other way.
It isn't really double, L'Stevo, if you think about it, because we say "a friend of mine/yours etc", not "a friend of me/you". By the same token we need the possessive form "John's", not "John".
"She is Antonio's friend" is correct, but it's not expressing the same thing.
I would use that form either if I were implying that "she's ANTONIO'S friend (not MY/JOHN's) friend", (so here it would be the answer to the question "Whose friend is Ana?"), or to give the idea of only one friend, because I'm giving it the meaning of "special friend/girlfriend" as in "Who's that girl/Ana?" "She's Antonio's 'friend'."
"She is a friend of Antonio's", however, would be the normal answer to the question "Who is that girl/Ana?" and it's simply stating that she is one of Antonio's several/many friends.