I am sure that you have the information but in case you don't here is what I have.
Father: Lawrence Cockshot b Abt 1817 in Manchester, Lancshire, England d 18 Aug 1886 in Audrain, Missouri, USA
Mother: Mary Martha Galloway b Abt 1820 Over Darwin, Lanchire, England d Abt 1880 Tauton, Randolph County, Missouri, USA
They were married: 14 Sep 1840 in Lancshire, England
Lawrence came here in 1862 Nart cane ub 1863
On the 1900 census it says that Elizabeth came in 1863 but haven't been able to find her on any passenger lists.Some reports says she married in England in 1863 others say she married in 1863 in Illinois, USA
If this is new information I hope it leads you in the right direction.