One of those letters, which have kindly been sent to me, refers to a James Sym, a long-term resident of Sheboygan, Wisconsin, USA, who instigated in 1890 an enquiry into the estate of his uncle Alexander Sym [sic] of Collooney.
There is a family in Sheboygan Falls, Sheboygan, Wisconsin in 1880 comprising
James Sims, 65, born Scotland; wife Elgin Sims, 65, born Scotland; widowed son James Sims, 43, born Scotland; James Sims, grandson, 13, born Wisconsin; George Sims, grandson, 8, born Wisconsin; Elgin Sims, granddaughter, 6, born Wisconsin; son Robert Sims, 23, born Wisconsin.
James Sym, son of James Sym and Elgin Menzies, was born 2 August and baptised 18 September 1836 in Gorbals parish.
So it looks as if James Sr would have been born about 1814 or 1815, so he could be a brother of Alexander Sim Jr who was born about 1820. I haven't found them in Wisconsin in 1850 or in Scotland in 1851 so they probably emigrated about 1850, just too late to be enumerated in Wisconsin, and just in time not to be enumerated in Scotland (how annoying is that!). Now if there is a death certificate in Wisconsin, and if it names James Sr's parents, we might then know the names of the parents of Alexander Sim Jr.