Sorry, if my question was not clear, behindthefrogs. I was trying to establish what the spelling was on the original document, rather than the various transcriptions on various electronic sources, which are as listed in my original mail. As you stated, there are a number.
Jane's kind response did not clarify whether or not she had checked this is in the original Greasley records by confirming that the register said FAUKS, or mentioning her source. Once I can be sure of the phonetics of the surname, it may help me to establish which family in the area she may be the daughter of.
Over many years, I have run into issues that many parish records have been mistranscribed and sometimes the suggested family name or close variants online are not close. Early transcriptions, not revieiwed, have lived on for years with errors. A breakthrough has occurred after the original record has been reviewed, or kindly forwarded as a mobile phone image (for example) for me to review. A short name, that could be read as FAUKS, with poor script, could be something different (e.g. EALES, HALLS, HAWKS, GALES, etc).
I have returned to this conundrum after about 20 years after no progress in online source for Judith's parents (or possibly an earlier marriage). Unfortunately, I am not UK-based and rely on the kindness of Rootchatters who maybe in the position to help.
Pending Jane's clarification, I would still appreciate a review of the original record if anyone is in a position to do so, and if an image is available so I can check the script.
Thanks & regards,
Mark