Lancashire Birth indexes for the years: 1844 MATHER Mary ROPER Western Bolton WB/10/18
MATHER, MARY ROPER GRO Reference: 1844 M Quarter in BOLTON UNION Volume 21 Page 133
Richard and Elizabeth's other daughters (before and after) were born in Sharples, so its liklely Mary was too, but birth registered in Western Bolton. Probably died young as no baptism.
Missing in 1851, assumed died, but perhaps immigrated to the USA or of another family. She was born very soon after the previous daughter, both with MMN = ROPER, so another possibility that the birth was registered twice.
There are no matching child deaths for a Mary born 1844