1. He no longer lives here.

2. He doesn't live here any longer.
3. He doesn't live here anylonger.
4. He no more lives here.
5. He doesn't live here any more.
6. He doesn't live here anymore.
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Are they all grammatical? I can see 'anymore' in the dictionary, but I can't find 'anylonger.'

anylonger isnt a word

3 and 5 are incorrect. The others are fine.

Out of the given options, the grammatically correct sentences are:

1. He no longer lives here.
2. He doesn't live here any longer.
3. He doesn't live here anymore.
5. He doesn't live here any more.
6. He doesn't live here anymore.

As for your specific question about "anylonger," it is not a recognized word in standard English. The correct form is "any longer," which is an adverb phrase used to indicate the cessation of a previous situation.