I'd guess he is doing this because he wants people to think he is the good guy and didn't act badly..
Mostly people do that to deflect the attention away from themselves.. its a form of insecurity too.. he wants people to not think badly of him..
All you can do is just correct the lies whenever you hear them. Oh and maybe tel him you know he has been doing this and that its unacceptable.
he still love you. how about you?