To believe sis(12) over SD(11)?

This. Don't banish anyone. Treat them both as if they were your own kids, which in some ways they are. You need to get to the bottom of it, one of them is lying, but equally, you love them both and want to sort it out, as you all enjoy the setup and you don't want it to change.
I wonder if jealousy might be at stake here, from one of the - are they vying for your affection? Is one of them thinking that you prefer or show favoritism to the other? Could be SD feeling insecure, and being jealous of your perceived preference for your own sister (evidenced by the fact SD is the one you would immediately banish).

Firstly good for you to step into parent the girls when their parents aren't around.

Agree with others this is parenting. You don't need to pick sides but establish and reinforce boundaries. It will become clear which one is breaking the rules.

Make it clear that these messages are disgusting and noone is to ever send anything like that again to anyone. Explain that you know someone is lying (look them in the face when you say this) but you can't tell which one of them it is. Then say something like "You are allowed phones because I permit it, but if this behaviour happens again then the house rule will be that phones are given up at bed time/ or only used in the common areas".

i know this isn’t your question but I am shocked that neither of them have passwords on their phone. That is basic security 101. It opens them up to all sorts of risks. You/the parents can know their passwords but they should have them. And this problem would not have occurred if they had passwords.

Haven't read all the replies and this is probably considered bad parenting- but surely what D is trying to achieve is either a) that your sister doesn't come stay with you when she's around or b) she doesn't want to see your sister at all
SD is adamant that you dont speak to sis so you could easily nip the whole situation. In the bud bu telling SD that your sister will still be coming to stay with you and you wouldn't mind if she stayed with her grandparents when your sister is around.
Would avoid you dealing with anything or taking sides though. Although SDs reaction might reveal more.

I think your SD is at a tricky age, is probably very insecure, doesn't have a mum and probably feels like she might get pushed out by your sister, who she sees as a rival for your affections and something that disrupts what to her is the only family unit she's got. She doesn't have any mother figure in her life except you and she's terrified that she'll be replaced.

If she has lied then obviously that's not good behaviour, and clearly her fears aren't rational, but equally she's only an 11-year-old kid and I think it's pretty easy to see where all this might have come from.

I absolutely do not think you should send her off to her grandparents. She's already been rejected by her biological mum. I don't think you have to choose between your SD and your sister.

As PP said, in your situ I would be confiscating both phones until one of them told the truth and I wouldnt let them stay over at the same time again either

I still don't think it sounds like DSD definitely did write them.

I think you don't believe either of them, have a chat with both of them and remove phones when they are both there and don't give them back until the morning. One of them is lying and you have no idea which, you may think you know but you don't and you could ruin a relationship with one of them.

You have to treat both girls the same. If they were your daughter's would you automatically believe one over the other? I would sit them both down and have a conversation, and make it very plain that you will not tolerate nasty behaviour or lying. If neither owns up, then you take their phones away, and tell them that until someone tells you the truth, then you will be keeping both phones. Phones going forward are kept downstairs or on your bedroom at night.

Sorry, cross post. Ok, it does sound like DSD wrote them then.

Her dad needs to have a serious chat with her.

I would get them both together in a room and look them in the eye and tell them this needs sorting out. I think you'll be able to tell who's lying. If you can't prove it either way, you can't just decide that your SD is lying. I wouldn't be sending her to her grandparents but I would be taking both phones at bedtime and keeping them with me so there can be no repeat behaviour.

I would talk to sister face to face.

You know both these girls and we don’t. What would DSD achieve by banishing DSIS? More attention?

You said the messages didn’t read like they are written by sister, do they sound like something DSD would say? What was the nature of them?

Both these girls have had a tough time from the sounds of it. You really do need to get to the bottom of it though. I wish you luck.

But if she left them on there the sister would see them and probably have confronted the SD or told OP about it

if your sister has done it, then the messages will be deleted off her phone to cover her tracks. If your SD has done it, she wouldn’t delete the messages as she would want the evidence to be there to back up her story, surely?

To be fair to you it would seem a very weird thing for your sister to do, send your SD messages while she's sleeping in the same house as her. Has your SD got form for doing anything like this before?

Id this was my DC, I'd be confiscating both phones while at your house as they're clearly not mature enough to have them, they can have them back when whichever of them is lying comes clean.

When the pho was are returned I'd also be instigating a rule that the phones don't go upstairs at bedtime.

It’s a little bit irrelevant. Whether SD sent them to herself in an attempt to frame your sister or your sister actually sent them, they do not have a friendly or happy relationship and the current set up isn’t working.

Check your sisters phone.

I think OP is saying she thinks SD stole sister’s phone, sent the messages to her own phone, then deleted the sent messages from sister’s phone.

Which is quite a big con, does SD have form for this sort of thing?

Were they sent when your sister was at your mum's or at yours?

You don't need to choose anyone. If you had 2 children of your own and this happened you wouldn't be sending any of them off to grandparents. Your SD has shown you evidence so I would question why you are so inclined to believe your sister. Language used around adults as teens is different to the language used with other teens so I wouldn't see that as evidence she is lying.

You say 'messages' as if that will be universally understood.

What are they? Texts? WhatsApp? Snapchat?

I'm struggling to understand why establishing from where they were sent is difficult.

Where they text messages, WhatsApp, Snapchat?! What service or app where they sent on?

And how would SD be able to send them to herself?

I don't think you should take either of their words for it without any questions and thorough investigating.