After Ireland became a free state, they formed an army called Fianna Fail (FF) or Army of Destiny. Part of the agreement was for the British to supply the new army with weapons. Your rifle was one of those, so your information is correct. Other than that, it is a standard SMLE Mk III (or Rifle No. 1, Mk III), made by Birmingham Small Arms Co. in 1917 for the British Army.
In the 1950's Ireland sold off a lot of its old weapons in exchange with various arms makers and traders. They sold a large number of those rifles and got in return a [much smaller but sufficient] number of FALs.