Most interesting. Do you have any ancestors from Graigue (just south of Kilkenny City), St Mary's Parish in Kilkenny City or Slieverue or elsehwere in southern Kilkenny? My wife and I were in Cadiz recently and met a Murphy descendant whose ancestors come from Ballynakill. She is taking an autosomal DNA test so we will know whether we are related. You may be too!
FYI, there are quite a number of Murphys from County Kilkenny who went to Cadiz in the 17th to the 19th centuries.
i have a public tree on Ancestry.com, The Marvelous Murphy's, which traces my ancestors as best I have been able to find. I have no Frances Murphys to my knowledge.