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My grandmother was a Greening and I have recently started collecting as much information as I can about the family in Devon. Unfortunately I do not have anything on your William. Do you have any further details? When did he migrate? Was he already married? Did he have children? Where/when were they born?
I believe that the majority of Devon Greenings are desecended from William and Jasper (brothers?) who migrated from Gloucester to Bideford circa 1620-30. They became successful businessmen and were involved in, amongst other projects, maritime trade with places on the eastern Atlantic seaboard. In 1675 Samuel, possibly the son of Jasper, sailed from Bideford to Newfoundland on his ship "The Prosperous". There is also record of them trading in Virginia. At least two, both Richards, were lost at sea.
William, John and Richard are names that seem to appear in just about every generation of every family, which makes identifying individuals very difficult, but if you have any further details of your William, I will see if I can match him up.