Kay,
Statutory birth registration didn't start in Ireland till 1864. Prior to that you need to rely on church records. Not every church has records for the 1860s (Some Church of Ireland records were lost in the 1922 fire in Dublin) and where they do exist not all are on-line, so if you don’t know where in the county Ann came from it may be difficult to trace her. RC records are mostly on-line but for other denominations you might need to search the records in PRONI in Belfast which requires a personal visit.
What denomination was Ann, and what was her father’s name and occupation? Tradition was to marry in the bride’s church so that should be a clue as to her denomination.
Graham is a very common name in Fermanagh. For example, there are 548 in the 1901 census of the county, 39 of whom were named Ann, so care is required to identify the right family. (Most of the Fermanagh Grahams are descendants of Scots who moved there from the Scottish Borders in the 1600s).
You are curious as to when Ann moved to Lancashire. Most people who left Ireland then did so for work, so she probably left when she reached working age ie 16 -18. There were quite a few mills in Fermanagh and if she was working in a mill in Lancs then it's possible that she came from a mill/weaving background.
You say that John Maguire seems to be from Kildare. That could be so but it is also the most common surname in Fermanagh. (The Maguires were the original “native” tribe in that area). Perhaps he’s from Fermanagh too and they knew each other before leaving Ireland? (92 Maguire in Co. Kildare in the 1901 census. 2056 in Co. Fermanagh). Statistically he’s likely to be RC.