The Greenhalgh name is one that connects to the Hopkinson family numberous times. I have run across the work of Rae V. Hopkinson many times and she did a wonderful job of outlining all the Greenhalgh, Hopkinson and Coop connections in a chart HP242.chart only. My immediate Greenhalgh line is Thomas Greenhalgh, of Moss or Buckley Fold. He may have married Susan Holt. They had: Phebe (bc 1720), and probably others.
Phebe Greenhalgh (bc 1720) married 29 JUN 1742, Edward Hopkinson. They had: Thomas Hopkinson (b 16 MAR 1745), and perhaps others. See my Hopkinson page for their descedants.