I think Kay is right - Thomas Jackson was buried 27th May 1888 here in Garston - a year after they married and it looks like his widow Mary Ellen Jackson married William Monaghan 11th march 1889 - James Henry b 2nd feb 1890 - everything fits in - so I agree with Kay
Mary Ellen was a Hughes - not a Jones - she was born in Everton in 1867 and her parents were John Hughes and Annie in 1881- and they lived in Wellington Street,Garston ( quite posh then )
aha - he worked in the Copper works and he was from Holywell, Wales andAnnie was from Preston .The English didn't know how to work Copper - the Welsh did so a huge amount of Welsh were brought here ....
John Hughes
Event Type Census
Event Date 1881
Event Place Garston, Lancashire, England
Registration District West Derby
Residence Note Wellington Street
Gender Male
Age 38
Marital Status (Original) Married
Occupation Warehouseman In Copper Who Manufs
Relationship to Head of Household Head
Holywell, Flintshire, Wales
Annie Hughes Wife F 34 Preston, Lancashire, England
Mary Ellen Hughes Daughter F 14 Everton, Lancashire, England
Annie Hughes Daughter F 12 Everton, Lancashire, England
Jane Hughes Daughter F 10 Garston, Lancashire, England
John Walter Hughes Son M 7 Wallasey, Cheshire, England
Emily Hughes Daughter F 5 Wallasey, Cheshire, England
Joseph Hughes Son M 3 Wallasey, Cheshire, England
Frank Hunt Hughes Son M 2 Wallasey, Cheshire, England
Charles Wynne Hughes Son M 0 Wallasey, Cheshire,
need to see if that record of William Monaghan aged 21 being born Liverpool on his ships log is correct ? is so I doubt if Matthew is related unless he is a nephew of John Monaghan

added - looks like John Hughes married Annie Murray in 1864...West Derby ,Liverpool ?...needs checking out