A Lady Cyclist's Guide to Kashgar by Suzanne Joinson
I read this on my Kindle. Bought it ages ago but took a while to get around to it. It's exactly the sort of novel I love - a timeslip novel, with a story from the past being uncovered in the present. In this novel there's a mystery in the present which is revealed as you hear more of what happened in the past.
In the historical story set in 1923, Eva and her sister Lizzie, and a formidable missionary woman Millicent arrive at Kashgar in north-western China to set up a Christian mission. They try to help a young girl who's been outcast and is giving birth, but sadly the girl dies and Eva ends up taking care of the baby, while Millicent is accused of causing the girl's death. While under house-arrest, Eva starts writing her cycling guide to Kashgar (yes, she has brought a bicycle with her...)
In the present day story, Frieda unexpectedly inherits a flat-full of items from an old lady named Irene who she'd never heard of, but to whom she's apparently next-of-kin. Helped by a refugee Tayeb who's on the run, being an illegal immigrant, Frieda tracks down her mother to help find out who Irene was.
The book flips back and forth between the two stories. Both are completely absorbing, peopled by memorable characters who you really care about (except the deeply unpleasant Millicent, I guess) Kashgar and environs makes for an unusual setting - especially in 1923! Very satisfying ending.