1.根据句意,该句最好使用强调句型如下：
It was her father who/that bought the birthday present/presents for her.
或：It was her father who/that bought her the birthday present/presents.
2.当然用最一般的翻译方法也可以：
Her father bought the birthday present/presents for her.
或：Her father bought her the birthday present/presents.
注：/ 表示可以任意选用其一.