Another name for Elizabeth was Elizabeth Fairbanks.4
Are we sure she is Fairbanks and not Brook? The following web site (with examples) has her as Brook.
Elizabeth married James Beaumont, son of Richard Beaumont and Mary Drake, Apr to Jun 1850 in Huddersfield.1 (James Beaumont was born on 11 Jul 1828 in Almondbury, Huddersfield 2 5 and was christened on 20 Sep 1829 in Almondbury 6.)
FreeBMD Online Index of BMD, England & Wales, www.freebmd.org.uk, Marriages Jun 1850
BEAUMONT James Huddersfield 22 299
Brook Elizabeth Huddersfield 22 299
2 Family Register - Ian Beaumont 2003.
3 Ancestry.com Online Census and BMD, www.ancestry.com, 1851C. b Huddersfield.
4 Family Register - Ian Beaumont 2003, Elizabeth Fairbanks.
5 Ancestry.com Online Census and BMD, www.ancestry.com, Almondsbury.
The Church of Latter Day Saints, International Genealogical Index, www.familysearch.org/, Extracted from local records. JAMES BEAUMONT Male
Christening: 20 SEP 1829 Almondbury, Yorkshire, England
Parents: Father: RICHARD BEAUMONT Mother: MARY