“Let his/him come in.”

Let his come in is wrong.
Let his cat come in is right.
If the cat is a he then let him come in is also right. (him referring to the cat)

The word "his" is used in two senses, parallel to "my/your" and also to "mine/yours".

Let's not use "cat" in this example since cats are rarely capable of doing what we want them to. Let's use "child" instead.

That is my/his child.
That child is mine/his.

Let my child come in.
Let mine come in.

Let his child come in.
Let his come in.

Grammatically, I think it's fine in the right context.

In grammar, a sentence is the basic grammatical unit. It contains a group of words and expresses a complete thought. A sentence consists of a subject and a predicate. For example in the sentence "Bill writes good poems" Bill is the subject of the sentence and writes good poems is the predicate.

This is a mistake requiring the use of formal grammar.

the use of "Let ... come in" requires either a noun or a pronoun (ie one of these grammatical words that replaces a noun -eg when you want to avoid being redundant)

The issue with "his" is that it is not a pronoun such as me/you/him/her/it/us/they (and generally it is not a noun) in English, but, rather, a possessive adjective (as in "his book") or a possessive pronoun (replacing a possessive adjective and the noun that follows...).
Therefore 'Let his cat come in' can work, and then on its own 'don't let my cat in, but let his come in' could possibly work as an exception, though it is very heavy...

@fp2161 I don't even know the possible exception for 'let his come in'. It sounds strange.

I had some confusion regardig this matter. Thanks for explaining the fact simply with me!

"Let his come in" has 9 hits on Google.
"Let him come in" has 996,000.
So if your partner chooses 'his' instead of 'him,' he (or she) has a 1 in 110,667 chance of getting the job.

This is why language can't be taught from a book; it has to be heard to be accurately understood and repeatable--English far less so than, say, Mandarin, but here's one comparatively rare occurrence where emphasis and intonation are crucial to the meaning.

Or is that so rare, in English?

I just had such complicated questions..

In this context, "Let him come in" is the correct option. The use of "him" as the object pronoun is appropriate when referring to a person being allowed to enter. "Let his come in" would not be grammatically correct in standard English usage. Therefore, "him" is the most suitable choice for the completion of the sentence.

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