Hey there - dropping by with your requested review! Sorry about the delay - things in RL have been pretty busy recently, involving and moving and exams and stuff - but I'm here now, so it's not too bad! :)
I like how you've written Sirius. He seems pretty childish and immature - which is how he should be - and yet slowly sort of realising that maybe what he was taught wasn't right. At the same time, he's reckless - he tells a muggle about magic, which is technically an offence, I believe. Including Kreacher was a nice touch, too, as since we didn't see any of his other family, particularly Regulus and his dad who we know least about, it helped make the idea of the family more known. Plus it reminded me of OotP, when he hates being stuck in the house. I don't know if it was intentional, but it was good either way!
Lexi's character is interesting. I like how there's a reason for her to be called 'Lexi', other than it's a good name, how her dad left her mum and their family, how she's got so many sisters. I particularly like how she doesn't seem to be all that brave or strong, but really open to believing seemingly strange things. Again, it reminds me that she is just a kid at the beginning and they're more likely to believe things like that, you know?
The only thing character-wise I would say is to be careful to keep their situations as separate and different. Yeah, they both don't have great home lives, but they're going to have different peeves, different situations, the severity will be different. Right now, I guess just because you're kinda introducing it and keeping it simple, their lives seem a bit too similar to be totally realistic. It's a personal thing, though, but just something to bear in mind perhaps ;)
I did like her sisters, though, and the conversation between Lexi and Sirius via the letters was great! It was so like kids to talk like that, I could really imagine both of them.
Plot-wise, I think as long as you actually have a really good, solid reason for Sirius wanting to find Lexi again (because, honestly, most people would just forget about it or not go to the effort of finding her, and it's a bit extreme), then I think you're golden. I'm a bit sceptical as to how there was a hole Sirius could push parchment through into the other house given that it's stated in the books Sirius' dad put every known enchantment on it, other than the Fidelius Charm, but if you can make it work/explain it, then it's not a problem! It's just a little detail, it's not that important.
I think this is a great prologue - it does sort of start it all off nicely, introduce the characters well.
Oh, one quick thing: never start a sentence in prose with 'and'. It's grammatically incorrect. The same with 'but'.
So yeah, I like this. I think it's good so far, I like your characters, I think it's a good start, there is a lot of information in it but you manage it well, the letters are great, the flow and pace are good. Feel free to re-request in future! :)