Did they "remove to New Hampshire" by way of Holden, Massachusetts? There is a Daniel and Abigail Grout having a child Hannah there in 1771 (VR), and a Daniel Grout mentioned in the Holden town history and Mass. Soldiers and Sailors as being a Corporal in 1775.
(https://www.familysearch.org/ark:/61903/1:1:FCSC-56T : 10 November 2020), Daniel Grout, 28 Dec 1763; citing Marriage, Sudbury, Middlesex, Massachusetts Bay Colony, British Colonial America, Massachusetts Secretary of the Commonwealth, Boston; FHL microfilm 004198966.
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