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Based on reviewing the 1834 Tithe records and the 1857 Griffiths Valuation data for Kiltoghert parish, it is likely the surname was Farrell in Ireland.
RC records for Kiltoghert start around 1824. There are two possible parishes: Bornacoola and Kiltoghert.
Do you know if Michael married in Ireland? There are a number of Michael Farrell marriages in Bornacoola in the 1830s.
You may want to add Michael's story to our XO Chronicles site https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-data...
Have you considered autosomal DNA testing?