How to deal with constant lies and refusal to accept there is consequences for bad behaviour

[naneee]

My SD is 9 and has been living with us now full time for over 15months her behaviour has always been and still is quite challenging.
Without going into too much detail life at her mothers was very chaotic, no routine and structure and would even go as far as saying she suffered neglect from her mother. Which among other things that happened is what led to her coming to live with us.
She can be a very sweet and loving girl, so definitely has a hold of her emotions etc however she is very sly, when she thinks no one is watching or can hear she will be very manipulative to her Little sister, she will tell her to do naughty things then come and tell us what she's done to get her into trouble.
She will blatantly do something she shouldn't (sometimes in my presence) and when I pull her up on it she will completely deny she did it.
She will do something naughty then blame it on one of her siblings
Just seems like no amount of talking and patience will get through to her and struggling a little with how best to deal with it.
Any advice would be very helpful

Will also add that consequences was not something her mum taught her at home. So understand it will take time to get through to her and make her realise that actions does have consequences

Anyone got any advice? Pretty please, at my wits end

Has your SD had any counselling?

Is her younger sister a half sister? Could her behaviour be how she got attention from her mum and teachers at school? Young children often believe that negative attention is still attention so a good thing.

How's her behaviour at school?

All kids can do stuff like blame their siblings for bad behaviour but I'm guessing with her background it's not on the lines of "I didn't nick the last biscuit- sister did" when she's got chocolate all around her mouth.

No she hasn't had any counselling, social work isn't great in our area and still waiting to hear back about support for her..

I totally don't blame her at all, as I do think it is the only way she's got attention in the past but it's a vicious circle cos I can't ignore the negative behaviour, because don't want the other children seeing it be ignored and think it's ok..

No, I have 3 children and know exactly all the tricks they pull but it's definitely more than just that, it's more serious things and things that are deliberately done to get the other in trouble for no other reason than that

Younger sister is full sibling not half.

She has her moments at school too, but definitely been so much better since living with us hardly any bad reports and much more settled