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The Peter you are referring to is Peter (jr) Mooers/Moores, son of Peter (Sr) and Mary Pearson. There are LDS files at FamilySearch.org that claim Peter (Sr) as the son of Edmund (Jr) and Sarah Cooper. The problem with this link is two-fold: First, this may be entirely (and erroneously) based on someone's suppostion, the second, is that there is no mention of Peter in any of the birth records for Edmund (Jr) and Sara Cooper. I've been trying to establish this link through specific documentation, but to no avail so far. Undoubtably, Peter is linked to the Moores/Mooers of Newbury, MA, but as to his father no one yet knows. Edmund (Sr), widely accepted as the immigrant forefather of most Moores/Mooers in America (a supposition I do subscribe to,) came with his father Francis, and two brothers - Samuel and Matthew. He had 3 sons Jonathan, Edmund jr., and Richard. The truth is that any of the sons or grandsons of Francis could be Peter's father.
Some of the things that lend credence (at least to me) regarding Edmund (Jr) being Peter's father is that Sarah is from Rowley (where Peter was born,) Sarah's father was Peter Cooper,(naming children for mothers and fathers and grandparents is quite common,) and Edmund (Jr) had among his children 2 Edmunds listed, the first born 1677, the second in 1693 (which would make Peter roughly the same age as Mary Pearson.) Since birth, death, and marriage records are very sketchy during the early colonies in Massachusetts, we may forever have to rely on supposition to draw our conclusions.