先行词被the only,the very,the last,the just,the same 等修饰时,不管先行词指人还是指事物,引导词都用that.例如：
You’ve the only person that I met here.你是我在这儿遇见的唯一的一个人.
This is the very shirt that I am looking for.这正是我一直在寻找的衬衫.
所以,你的这个句子应该是：
He is the only one of the students that has been invited to the English Evening.