I found your family tree and it looks like you've found a lot of info since your posting.
I did find the following.
Patrick James Murphy
Born: Sept 24, 1841
Died: 9 July 1926
Burial: Ainsworth Cemetery, Ainsworth, Brown, Nebraska
If you're interested in his obituary, contact the historical society, www.usgennet.org/usa/ne/county/brownhistsoc.htm
. Successful Searching!