I have John L Jones 1810, Oswestry, Shropshire passing away in Pennsylvania 1894. Parents of his is unknown as we can't find a definite dob. I am unsure if he has a middle name initial of L as on the gravestone I noticed it had their names as J. & M. L Jones :/ Mary is born in Walesby, Lincs around 1814, her parents are John Bradshaw and Rebecca Turner. I found her baptism for 10 Sept 1815. But I have never been able to find her dob under either of her parents surnames for the area she was born in.
Re "J. & M. L Jones" - if it was in England, I would take the "L" as being one of Mary's initials, rather than John's. But in the USA? - I don't know.
I'm wondering what evidence you have that your Mary Bradshaw is the one baptised in Walesby in 1815, other than that the name matches. Walesby and Oswestry aren't exactly close, and Bradshaw isn't such an uncommon name. Before deciding on who her parents were I'd want to make sure I had the right marriage between her and John, as that could give significant clues to who her parents were and/or where she came from.
You mention the alternative surnames found in the immigration records (Bradshaw and Turner): I wonder whether rather than being her father's and mother's names, these might indicate that she had been marrried before, and are her own maiden name and that of her first husband. On the other hand, lots of people are known by more than one surname, possibly indicating something like illegitmacy or having taken a stepfather's surname - there are plenty of discussions on here about it. So unless there's a clear explanation for the alternative names, it's risky to draw conclusions from them.
I haven't spotted them, but I hope you have firm reasons for deciding John Jones was from Oswestry - there must be dozens of John Joneses to choose from, if not hundreds!
Arthur
