Her birth index:

Name:                         Mother's Maiden Surname:
SHARP, HANNAH MARIA           GREEN  
GRO Reference: 1852  M Quarter in HUNSLET  Volume 09B  Page 297
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In Q3 of 1878 an Anne Maria Sharp married either John William Arthur or John Eastwood Lishman in Leeds district.  One way forward is to get one marriage certificate and see if it is her father that is on it.  Another way forward is to look at the 1881 censuses fr the Arthur and Lishman families to see if the wives were Anne and if so, does she share the birth information of her unmarried days.
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In 1881 it looks like John William Arthur is the man except for one detail, that Anni M gave her birth as 1854, two year late.  But her husband’s birth was given as 1858 so she may have been disguising that she was six years older than him.  They were at Huddersfield Road, Wike aka Wyke, Bradford,  Yorkshire (West Riding):

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
John Wm   Arthur  Head  M  M  23  1858  Stuff presser     Halifax, Yorkshire
Annie M   Arthur  Wife  M  F  27  1854  -                 Leeds, Yorkshire
Mary A    Arthur  Daur  S  F   2  1879  -                 Leeds, Yorkshire
Thomas N  Stead   Vstr  M  M  30  1851  Engineer (e & m)  Leeds, Yorkshire
Polly     Stead   Daur  S  F   6  1875  Scholar           Leeds, Yorkshire
Ada       Stead   Daur  S  F   5  1876  Scholar           Leeds, Yorkshire

Ref:
Archive reference  RG11
Piece number       4426
Folio              109
Page               18
Combined:          1881 ref: RG11, piece 4426, folio 109, p. 18
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And there is no Annie M Lishman in the 1881 census so the above ‘must be’ her.
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In 1891 she had a further two daughters, making three in all.  They were then at Quarry Mount Street, Leeds, Yorkshire (West Riding):

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
John W    Arthur  Head  M  M  33  1858  Stuff presser  Halifax, Yorkshire, England
Annie M   Arthur  Wife  M  F  37  1854  -              Leeds, Yorkshire, England
Mary A    Arthur  Daur  -  F  12  1879  Scholar        Leeds, Yorkshire, England
Annie     Arthur  Daur  -  F   9  1882  Scholar        Leeds, Yorkshire, England
Florence  Arthur  Daur  -  F   5  1886  Scholar        Leeds, Yorkshire

Ref:
Archive reference  RG12
Piece number       3702
Folio              18
Page               29
Combined:          1891 ref: RG12, piece 3702, folio 18, p. 29
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The family was the same in 1901 with these Oxccupations for the three daughters: Nil (for the eldest), Dressmake, and Tea packer for the youngest.
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In 1911 the household was again the same though she gave the information that they had been married for 32 years, had four children of whom one had died.  They were living in a seven room house at 33 Hartley Crescent Woodhouse Leeds, Leeds, Yorkshire & Yorkshire (West Riding):

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
John William  Arthur  Head  M  M  53  1858  Stuff presser at kirks dyeworks woodhose  Halifax
Annie Maria   Arthur  Wife  M  F  57  1854  -                                         Leeds
Mary Ann      Arthur  Daur  S  F  31  1880  Tailoress                                 Leeds
Annie         Arthur  Daur  S  F  28  1883  Dress maker                               Leeds
Florence      Arthur  Daur  S  F  25  1886  Grey room                                 Leeds

1911 ref:  RG14 PN27011 RG78 PN1548A RD500 SD3 ED30 SN147

The ‘Industry’ column shows that Florence was working at Kirks Dyehouse, the same place as her father.
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Her and John’s children were:

Name:                  Mother's Maiden Surname:
ARTHUR, MARY ANN       SHARP  
GRO Reference: 1879  J Quarter in LEEDS  Volume 09B  Page 562
ARTHUR, ANNIE          SHARP  
GRO Reference: 1882  M Quarter in LEEDS  Volume 09B  Page 559
ARTHUR, MINNIE         SHARP  
GRO Reference: 1883  J Quarter in BRADFORD YORKSHIRE  Volume 09B  Page 9
ARTHUR, FLORENCE       SHARP  
GRO Reference: 1885  J Quarter in LEEDS  Volume 09B  Page 540

The last but one may be the fourth child who was said to have died before 1911 and did not appear in any census but it is odd that she was born, or registered, in Bradford.  But no other Arthur-Sharp births have been found in England.

The following looks stongly like Minnie’s death:

Name:               Age at Death (in years):  
ARTHUR, MINNIE      3  
GRO Reference: 1886  S Quarter in LEEDS  Volume 09B  Page 361

I think the evidence is complete that Minnie was their fourth child who died young.
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In 1939 none of them could be identified.  Probably Annie and John had died and possibly the daughters had married.

Her death index, with the same birth year as given in all the post-marriage censuses.:

First name(s)  Anne M
Last name      Arthur
Gender         Female
Birth year     1854
Age            72
Death quarter  1
Death year     1926
District       Leeds
County         Yorkshire
Volume         9B
Page           374
Country        England
Record set     England & Wales Deaths 1837-2007
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Their marriage index:

First name(s)     Anne Maria
Last name         Sharp
Marriage quarter  3
Marriage year     1878
MarriageFinder    Anne Maria Sharp married one of these people
                  John William Arthur, John Eastwood Lishman
District          Leeds
County            Yorkshire
Country           England
Volume            9B
Page number       431
Record set        England & Wales Marriages 1837-2005
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