You are correct, of course, MHT. But I always learned it this other way: for example, "A child born to him" (would therefore also be "to him and his wife"). Another example, third person: "The administration has given us</> students no alternative" (as opposed to "we." Remove "students" and you'd see "we" would be wrong "the administration has given we no alternative"). I was taught to complete a sentence with/without the word(s) in question.
"Him" is objective case, which is used following a preposition. For example, "Give it to me" ("me" is objective)--and, obviously, "Give it to I" would cause heads to turn!