"I know him a teacher"
doesn't seem like it can be right to me unless it's casual/conversational and there's some explicit or implied punctuation, like:
"I know him – a teacher" (i.e. "I know him, he's a teacher")
or
"I know him, a teacher?" (i.e. "I know him, is he a teacher?").
As has been suggested, something like:
"I know him as a teacher"
or
"I know him, he's a teacher"
seems more grammatically correct.
There could also be a difference between saying "I know him as a teacher" and "I know that he is a teacher", as the former is more likely to imply a relationship between yourself and the teacher - you are stating that this connection/relationship exists because he is a teacher (perhaps you know because he was your teacher once), whereas the latter could be used to describe someone who you have never even met or communicated with, you're just stating that you know they are a teacher, nothing more. However, this is not strictly the case as you could be talking about someone who is well known in the world for being a singer and actress, which whom you have no personal relationship and still say "I know her as a singer" because that's how you first became aware of the person - because they are a singer.
3"I know him *as* a teacher" would be acceptable, but I can't explain why you need the preposition as – Mari-Lou A – 2016-12-21T10:34:10.350
3I don't think the omission of to be (I know him to be a teacher) is necessarily ungrammatical, but it sounds very archaic. – Jakub – 2016-12-21T11:12:57.773
2"One that goes with him: I love him for his sake; And yet I know him a notorious liar, Think him a great way fool, solely a coward;" All's Well That Ends Well, Shakespeare. But I think we're encroaching on the ELU territory. – Jakub – 2016-12-21T11:33:14.807
2@Jakub - I wouldn't call that "ELU territory." I think you're simply (and correctly) pointing out that the construct might work as a literary, poetic, or archaic construct, but not in contemporary conversation. – J.R. – 2016-12-21T11:35:52.400
1@Mari-LouA "I know him as a teacher" works, but is slightly different from "I know that he is a teacher". "I know him as a teacher" implies that, while he may have many other traits, you only know him as a teacher. "I know [that] he is a teacher" implies that you know the fact that he is a teacher. – Harrison Paine – 2016-12-21T15:22:36.703
@HarrisonPaine yes, well the OP mentions that sentence too, but he's asking about using the object pronoun, him, and my comment (not an answer) was just that, an observation. – Mari-Lou A – 2016-12-21T15:40:23.747
@Mari-LouA I'm just reminding that "acceptable" doesn't mean "same meaning". "I know him as a teacher" is indeed acceptable English, but might not always be an acceptable replacement for "I know that he is a teacher". Like everything, it depends on context. – Harrison Paine – 2016-12-21T15:47:30.510
I'm not sure you even need to include "I know" as part of your sentence -- saying "He is a teacher." indicates that you know, and is very simple and clear. The only reason to include the fact that you know explicitly would be in the context of other people indicating that they did not know him. – Gus – 2016-12-21T20:04:28.827