Which one is correct?
So, someone has asked you to wish someone else a Happy Birthday, right?
In that instance, both are correct.
You can say: "Wish her a Happy Birthday FROM us" specifying who is sending the greeting (us); or, "Wish her a Happy Birthday FOR us" specifying that someone is asking you to do a favour for them
The two or bunch of you are wishing someone else a Happy Birthday right? If so then it is "Happy Birthday from us."