Is it correct to say that is he or that is him?

Answer 1

No! that is not grammatically correct because you have forgotten to put the preposition. You should write this "this is for him"

In some contexts 'for' is not necessary.

If we are waiting for my brother to pick us up I could say to you "This is him. Let's go."

Answer 2

My understanding is that you would use she or he. See this example:

"Who was the person who stole your purse, ma'am?" The officer asked the victim.

She pointed to the third man in the line-up, "It is he. He stole my purse."

The reason we use "he" instead of him is that we are describing a person who did something or for identification. For example you would not say: "It is him. Him stole my purse."

Him is an object pronoun. For example. "I stole the wallet from him. It is his wallet." You would not say, "I stole it from he, it is he wallet."

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The above is excruciatingly correct. Proper English requires the subject pronoun after a copula ( e.g. is). However, English speakers generally use the object pronoun in informal speech, saying "it's me!" rather than the formally correct "It is I." This is because word order rules English grammar nowadays, not inflection, and the subject pronouns are understood to go before the verb and the object pronouns after it. So the real answer is: We write "That is he," but we say "That's him."