Assuming it's the right family, I found George Henry Morgan living with his wife, Sarah (born in York), and daughter, Frances (born c1879), in Hulme, Manchester, in 1881. George was a painter. Here's an Ancestry link if it helps – try as I might, I could not find the same record on FamilySearch – grrrr!
They had moved to Chorlton on Medlock by 1891: Ancestry (sorry)
I searched FreeBMD to look for George and Sarah's marriage and found these entries from Dec quarter of 1876: George Henry Morgan and Sarah Ann France.
(If you search gro.gov.uk there was a birth of a Frances Morgan registered in 1879, mother's maiden name France.)
Ancestry has this marriage in its Manchester marriages database. The parish register (St Mark's, Hulme) gives George's father's name as Peter Morgan, a slater. It says George was a warehouseman at the time of his marriage.
As I think someone else found earlier, someone who seems to be the right George (age 10) was living with his mother, Mary (a widow aged 27) on Bootle Street, Manchester, in 1871. Mary was also born in Manchester. Ancestry link (I really don't know why I can't find these on FamilySearch)
There was a death of a Peter Morgan, age 32, registered in Salford in the June quarter of 1870 so that might be worth following up.
I had a quick look for the birth registrations of George Henry and his sister, Eliza (born c1863 in Manchester) but didn't find them.
Maybe you can try looking for the baptism of a George Henry Morgan with father Peter?
