Both of my step children are chronic liars. I have come to accept that if their mouths are moving, they are probably lying.
I think that being split between 2 homes where the parents cannot and do not co-parent effectively can have this effect on children. I used to lie as a child, (as I’m sure all children do,) but my parents would work together to stamp the behaviour out.
In a situation where the parents are not doing that, but instead one or both of the parents are actively or inactively rewarding the lying (and a reward to a child can be as little as just receiving more attention for the lying) I can see this behaviour bedding in.
I think it is a common and unintended consequence of high conflict divorce and a step parent cannot undo it.
Practically speaking, here’s what to do: let the CMS claim roll in and make sure your husband lets them know about all other children in your house, including your other step child. The amount will be found to be nil, or negligible. The ex will regret ever tangoing with the CMS. They are inept and bring nothing but stress.
Try to avoid being alone with your SS. Don’t write him off yet either. 15 is old enough to know better but by no means fully grown. In another 15 years, you might have a really fulfilling relationship with him and his own family.
Try not to run him down to his father - it will break your marriage and it’s not worth it.