I'm in a similar situation, except that I have two children when OH has none. When I met him, DS was 5 and DD was 8 and he got along brilliant with DS but struggled with DD. It got worse when she started to act like a typical teenager but by the time was 14, she was over it and they started to get along great.
Unfortunately, the opposite happened with DS. DS went through the stage of talking back, being rude, hormones flying about so door slamming etc... and added to the fact that he treats his bedroom as a sty, OH started to really dislike him. This has led to them not communicating.
In a way, this is working as we all have a very busy life and so contact is not that frequent anyway. They will address each other, but beyond the good morning, how was school, there is nothing there. What does upset me is that DS who is now 14 has turned the page. He still has his grumpy moments, but isn't rude any longer and he actually is a teenage boy to be proud of, reliable, doing amazing at school. The state of his bedroom is still an issue but he is getting a bit better gradually. Unfortunately, it feels that the damage has been done at the moment, so neither of them are willing to make an effort to get their relationship back on track. I do understand DS not wanting to make an effort, after all, it is DH who took the step back, and DH is not yet at the stage where he can fully appreciate that DS is a great lad.
However, DH has admitted that some of his friends have exactly the same issues with their own boys, so it's not so much a step issue and as a matter of fact, his best friend has it much worse, even though he used to be extremely close to his boy.
I feel confident that once DS is over adolescence, they will gradually become close again as DH has with DD. I am always keeping an eye on DS so that this is not affecting him emotionally, especially the difference in behaviour with his sister, but so far, he is showing no distress by it.
I make sure that I treat him no different to how I would regardless of the situation, ie. picking him up on his behaviour, but always reminding him that I am totally dedicated to being his mum and loving him dearly as I always will regardless of his behaviour.