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From what @Soul says, you just treat whatever slice of the place she's buying as a purchase. So if that chunk is large enough to breach the stamp duty limit, you have to pay. But the slice we're talking about isn't big enough to breach that limit.
I'm sure I'll get a proper steer from the conveyancing solicitor in time - they're the ones who handle the calculation and payment of stamp duty, right?
How does the stamp duty work, I presume you can gift her the part that you own equity on, but its the mortgaged part that she is buying from you that is eligible for stamp duty? Is that correct?