From the Morning Advertiser, Saturday 07 December 1872:
Francis Edward Knibbs, of New York, USA., to Matilda, daughter of Matthew Potts, Esq., of London, England.
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From the Pall Mall Gazette, Friday 06 December 1872:
KNIBBS-POTTs-At St. Mary's, Bow, Mr. F. E. Knibbs, of New York, U.S., to Matilda, daughter of Mr. M. Potts, of London, Dec. 3.

I don't quite follow these newspaper articles. It seems too much of a conicidence for it to have been another Francis Edward Knibbs marrying a girl with the surname of Potts, and a father named Matthew, also from London.
I'm not aware of Francis having been to New York, but I'm guessing that he may have gone there for a while to work.
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From The Week's News, 7 December 1872:
Knibbs-Potts-At Bow, F E Knibbs to Matilda, d of M Potts, Dec 3.

In 1851, we see Francis Knibbs, aged 12, living at Market Place, Shepton Mallet, Gloucestershire, England with his aunt and uncle George and Selina Witcombe (nee Best) and their son Jonah aged 17. George was a Cabinet Maker.
George Witcombe Head Mar 40 Cabinet Maker Somerset Downhead
Selina Witcombe Wife Mar 42 Somerset Dinden
Jonah Witcombe Son Unm 17 Cabinet Makers Apprentice Somerset Shepton Mallet
Francis Knibbs Nephew 12 Scholar Middlesex Ratcliffe

We assume that George, Selina and Jonah are relatives on his mother Ann's side of the family.
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I believe in 1861, Francis took over the running of the Royal Oak public house at Plumbers Row, Mile End, London.
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Francis was quite possibly living in the Kings Arms in West Street, Buckingham in 1864.
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From the South London Press - 17 July 1875:
Transfer of Licenses - Newington.
St. OLAVE. - Royal Oak, Tooley-street, Francis Edward Knibbs to Thomas Johnson.
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Francis appears in the 1881 census living at 146 Armagh Road, London, England:
Francis E KNIBBS Head Mar 42 Publican Shadwell Middlesex
Amelia KNIBBS Wife Mar 39 Holborn Middlesex
Francis KNIBBS Son 6 Scholar Southwark Middlesex
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Francis can be seen in the 1891 census living at 103 Tredegar Road, Stratford le Bow, London, England:
Francis Knibbs Head 52 Living on own means London St Georges East
Amelia Knibbs Wife 49 London Holborn
Francis Knibbs Son 16 Stationers Assistant London Southwark

also,

Name Relationship Age Gender Birthplace
Francis E Knibbs Head 52 Male St George In The East, London
Amelia Knibbs Wife 49 Female Holborn, London
Francis Knibbs Son 16 Male Southwark, London
Mary Lorkin Lodger 35 Female St Luke, London
Emma Chatterton Boarder 25 Female Birmingham, Warwickshire
Ellen Cooker Visitor 30 Female Hatfield Broad Oak, Essex
Town: Bow and Bromley of the Tower Hamlets, Ecc. Parish: St Stephan, Civil Parish: Stratford Le Bow St Mary, County: London
Registration: Poplar, Bow, 6
Source: PRO/National Archives Reference # RG12/314 Folio 129 Page 10
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Francis died aged 61 years
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Knibbs Francis Edward of 103 Tredegar-Road Bow Middlesex died 29 September 1899 Administration (with Will) London 6 November to Amelia Knibbs Widow Effect £2104 5s. 3d.
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From the Eastern Post - 10 October 1899:
Death of Mr. Knibbs Sen,
At the meeting of the Bow Vestry on Tuesday evening MR. KNIBBS, the chairman (Mr. Mark Dalton) announced, with regret, the death of Mr. Knibbs, sen., father of Mr. Knibbs, the assistant clerk, who, on account of this great bereavement, was absent that evening. He moved that a message of condolence be forwtrded to the family.
Mr. Gillard seconded the motion, which was carried in respectful silence. Mr. Knibbs was an old resident in the parish, and took a great interest in parochial affairs.

Amelia's parents can be seen in 1841, shortly before she was born, living at 18 Brook Street, Holborn. London, Middlesex:
Mathew Potts 50 Pocket Book Maker
Henry Potts 11
Tom Redding 20 Apprentice Book Maker
Mary Potts 40
Emma Potts 6
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In 1851, we see Amelia living with her parents still living at 18 Brook Street, Holborn, London, Middlesex:
Mathew Potts Head Mar 65 Pocket Book Maker Swallow Street Regent S Middlesex
Mary Potts Wife Mar 50 Cripplegate
Emma Potts Daur 16 St Andrews Holborn
Amelia Potts Daur 10 St Andrews Holborn
Henry Potts Son UnM 21 Pocket Book Maker St Andrews Holborn
Thomas Potts Grand Son UnM 16 Kensington Surrey
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In 1871, Amelia was living with her widowed mother, at the household of Amelia's older sister, Emma. Emma had married a man named Charles Gillett Payn during q2/1860 at Islington District, London, Middlesex. They were all living at Myddleton Street, Holborn, London, Middlesex:
Charles G Payn Head Mar 36 Taylor Somerset Long Sutton
Emma Payn Wife Mar 35 Middlesex Holborn
Charles H Payn Son 10 Middlesex Clerkenwell
Emily Payn Daur 8 Middlesex Clerkenwell
Herbert E Payn Son 2 Middlesex Clerkenwell
Minnie(?) C Payn Daur 2mnth Middlesex Clerkenwell
Mary Potts Mother in Law Wid 70 Middlesex Holborn
Amelia Potts Sister in Law UnM 29 Middlesex Holborn
Caroline Driscoll Serv UnM 14 Middlesex Holborn
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The 1901 census shows Amelia living in the parish of Stratford Bow, London, England at 103 Tredegar Road:
Amelia Knibbs Head Wid 59 Living on Own Means London Holborn
Francis Knibbs Son UnM 26 Asst Boro Council Clerk London Southwark
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Amelia is given as her son Francis' next of kin in 1912, during a visit he made to the USA.
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We see Amelia in 1911, living at 103 Tredegar Road, North Bow, Poplar, London, Middlesex, with her son Francis:
Amelia Knibbs Head 69 Widow Private Means Holborn London
Francis Knibbs Son 36 Single Accountant Beremondsey London
Ann Maria Clarkes Servant 57 Widow General Domestic Servant Ollbury N Birmingham

The census states that Amelia had 2 children one of whom died before 1911.
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Knibbs Amelia of Belmont 32 Clifton-road Paignton Devonshire widow died 2 December 1934 Probate London 13 March to Hubert Ernest Payn taylor and Minnie Cecelia Brown widow Eddects £6050 15s. 4d.