Hi Jennie and Anne,
I discovered the will of William Beggs on PRONI's will calendars. I still do not know who his parents are, but am still searching. It seems that my part of the family was from the Ballyfrench/Ballyhalbert part of County Down and of the St. Andrew's parish. If you happen to find any connection between your Beggs and mine, please let me know.

Regards,
Amelia