He can come visit Canada and stay with you in January. The border agent will probably just let him in as a visitor and not give any restriction as to how long he can stay, which would mean he can stay 6 months. About one month before that time expires, he applies to extend his stay. He is not landing in January in the immigration sense, by the way.
If he gets the extension, he can stay until November. Then when he leaves and then returns, he is once again just coming in as a tourist or visitor from a country where a visitor does not need a visa. You should have proof of your PR application with you when he returns in November. There should be no problem getting back in.