The only way this will get better is if BM stops believing it and shuts him down every time he does this. That's between your SO and BM, they have to sort it out - don't sit down with them to talk about it, they are the parents and need to address this and you don't need to be part of it. In the meanwhile, do everything you can to not be alone with this kid at all, and see how your SO handles it. Don't stick around if the problem isn't addressed - this kid will only get better at lying. 

She is spot on. This is for the parents to handle.

Moving forward: disengage.  There should be no point in the future where it is you and the little liar alone.  If little liar starts claiming that you are abusing him, it could turn ugly fast.
 

Never be alone with him.  Always have your SO there so he is a witness.

If SO doesn't like that you won't babysit the little liar?  Too bad.  He's failing as a parent and his kid is a risk to you. He and the BM need to get the kid under control.  

In the meantime, you might also want to think long and hard. At 9, you still have the very difficult preteen and teen years ahead.  If your SO isn't working hard to get a handle on his son now, you have years of pain ahead of you.

Let the parents handle it, but I'd also consider putting in some cameras just so you can record what SS is saying to show him and BM that it's crap. I'd also spend exactly zero time with SS and would stop doing fun things with him, explaining that his lying is the reason why.

Ultimately, though, your SO is in a rough spot with the oldest. While he can fight for custody and parenting time of the youngest, he is a bit at BM's mercy with the oldest since he isn't legally his father. If your SO hasn't already, he needs to mentally prepare for the day that SS no longer gets to come over.

Honestly, too, I'd be nervous about an unrelated SS who lies coming over to begin with. While you didn't believe that the BF was hitting him, that doesn't mean BM won't believe him when he inevitably says the same thing about you. That's why you need cameras and need to never be around him alone. If he has learned to cope with a crazy mother/separation with lying and playing sides, then it wouldn't take much for him to escalate to a big lie to get something he really wants. 

Your SO and BM DO need to sit down and work this out without you or BF there. But, my guess is that the conversation won't go anywhere and SS will keep doing what he's doing. So, protect yourself.

This EXACT same thing happened to me when SD was 8. We had just changed to 50/50 custody. SD would come to our house and act like she was sooo excited to be here. She would bash BM's boyfriend and his kids. She would say things also like "I wish you were my real Mom." DH and I were naive and thought SD was actually feeling this way. 

Turns out BF called DH one day out of the blue. He started off the conversation about how he cares about SD but knows she is lying about somethings. Apparently, SD was going over the THEIR house and saying "All _____ does is sit on her phone" (at the time it was summer and I was taking her to the pool EVERYday "_____ always sends me to my room." "She yells at me." "She doesn't do anytihng with me." 

I was PISSED after DH told me this. I confronted SD as soon as she walked in the door. I asked her why she was lying and saying untrue things. I let her know that the households talk and we know what she is telling BOTH parents/families. She started crying. She got caught. I explained to her how lying to both US and BM only hurts everyone's feelings involved and gets people upset. We talked about what "stirring the pot means." Like I said, she was extremely upset when we talked to her, but it had to be done and I wasn't going to let me name get smeared. This was a hill to die on for me. Looking back, I should have discussed further with DH first, but I had to get my point across. After that, we never heard of SD making up these lies again. We also continued to shut down ANY negative talk about BM. Best of luck. 

Nothing good is going to come out of this relationship. You are spend time and money on a kid who has a BM and BF what you or SO are not.   Going through this cr*p for a non related child would be too much for me.   Let him stay with BM and make life easier for your family 

Kids can be really manipulative. Also, some kids are really sensitive to the need for their parents to hear certain things, so they default to saying what they think that parent wants to hear.

The BM in my life is "high conflict". We rarely speak of her and if she comes up, I give a vague, positive affirmation and move on. DH responds in appropriate adult ways when issues are raised - correcting misinformation and reminding Skids that some issues are adult issues and therefore, none of their business. BM, on the other hand, has made it clear to Skids that both DH and I are terrible people and she is the victim. One SS told all who would listen how DH and I just sit around talking about how much we hate BM when he is with us. This caused us no end of drama because DH's dumbo of a brother believed the kid (BM called DH's brother and said "oh, please talk to SS, he is so upset about his dad" and dumbo brother did so, in secret, without telling DH). MIL also got involved. It has ruined my relationship with both of them and severely impacted DH's relationship with them (they are both boundary-less, manipulative people and he is used to the way they act, so he is more forgiving and more used to their behavior).

I now avoid that Skid for the most part. He is in high school now, but I met him since he was 9 and he has always been manipulative and one to stretch the truth. He has also cheated (or attempted to cheat) at every game we've played and is constantly playing the victim, so it's not just when it comes to BM. 
 

To make matters worse, he lies to BM and then BM adds her own exaggerated spin to the tale in the retelling. It's a no win situation and I don't try to share the truth with others anymore...even DH's family.