Some thoughts for you
Law in just 6 civil parishes and 14 townlands in Co Tyrone listed in
1823-1837 TITHES APPLOTMENT BOOKS based upon the index work of the Irish Genealogy Hub’s listing for each parish in Northern Ireland, The relevant original books are in the Public Record Office of Northern Ireland (PRONI) Belfast .Each entry is one liner giving head of household only. The tithes are notorious for being biased and incomplete
COMBINED WITH
Law in 8 civil parishes and 13 Townlands with Griffiths valuation in the approx. year
1860 GRIFFITHS VALUATION at quick
www.failteromhat.com/post1845.php then for map references and more details use
http://www.askaboutireland.ie/griffith-valuation/produces a list that is laid out by civil parish in Co Tyrone, in an attempt to narrow down the large search possible
Law, Andrew Townland: Leboty Year: 1833 Aghalurcher
Law, Charles Townland: Leboty Year: 1833 Aghalurcher
Law, George Townland: Leboty Year: 1833 Aghalurcher
Law, Matthew Townland: Drummeer Year: 1833 Aghalurcher
Law, Thomas Townland: Drummeer Year: 1833 Aghalurcher
Law, Charles Townland: Killmore Year: 1833 Aghalurcher
Law Charles Town Parks of Strabane Camus GV~1860
Law Patrick Town Parks of Strabane Camus GV~1860
Law, Mr. Tl: Campsey Yr: 1827 Cappagh
Law, Daniel Tl: Galboley Yr: 1827 Cappagh
Law Matthew Claremore Clogher GV~1860
Law, James T: Cavanacark Y: 1825 Clogher
Law, Matthew T: Cavanacark Y: 1825 Clogher
Law, Matthew, Sr. T: Cavanacark Y: 1825 Clogher
Law, William T: Tullyvernaw Y: 1825 Clogher
Law, John T: Knocknacarney Y: 1825 Clogher
Law, Matthew T: Letbeg Y: 1825 Clogher
Law Matthew Latbeg Clogher GV~1860
Law Matthew Lislane Clogher GV~1860
Law, Robert T: Lislane Y: 1825 Clogher
Law Matthew Lislane Clogher GV~1860
Law Stewart Castletown Donacavey GV~1860
Law Stewart Racpane Donacavey GV~1860
Law Stewart Town of Fintona Donacavey GV~1860
Law, John T: Dullaghan Y: 1834 Dromore
Lawe Irvine Dullaghan Dromore GV~1860
Lawe Mary Dullaghan Dromore GV~1860
Law Martha Omagh (Town of Omagh) Drumragh GV~1860 map ref 88 she sublets 86,87 to John Robinson and Joseph Osborne
Law John Clunahill Glebe Longfield West GV~1860
Law, Robt. T: Bomacatall Y: 1826 Longfield West
Law, Saml. T: Bomacatall Y: 1826 Longfield West
Law, Jas. T: Gortnagarren Y: 1829 Pomeroy
Law, Jno. T: Gortnagarren Y: 1829 Pomeroy
Law, Robt. T: Cavanakeeran Y: 1829 Pomeroy
Law Robert The Diamond,Pomeroy,(Cavanakeeran) Pomeroy GV~1860
Law James, Jr. Gortnagarn Pomeroy GV~1860
Law James, Sr. Gortnagarn Pomeroy GV~1860
Law James Ballyfatten Urney GV~1860
Law Patrick Ballyfatten Urney GV~1860
now seeing I have one Daniel above I had a quick look at Moore and Muir in the tithes, No muirs found, leaving 241 Moor and Moore if by chance Daniel met his wife in the same parish as he lives, then her parents could be
Moore, Archd. Tl: Termority Yr: 1827 Cappagh Tyrone
Moore, Jas. Tl: Lislimnahan Yr: 1827 Cappagh Tyrone
Moore, John Tl: Mayne Yr: 1827 Cappagh Tyrone
Moore, John Tl: Tatteraonity Yr: 1827 Cappagh Tyrone
Moore, William Tl: Cranny Yr: 1827 Cappagh Tyrone
Moore, James Tl: Cranny Yr: 1827 Cappagh Tyrone and Fermanagh
Moore, Newman Tl: Aughagallon Yr: 1827 Cappagh Tyrone and Fermanagh
Moore, Thomas Tl: Cranny Yr: 1827 Cappagh Tyrone and Fermanagh
I read Omagh as a suggestion by someone living in Omaghs civil parish are
Moore, Anne T: Clenabogan Lower Y: 1830 Drumragh Tyrone
Moore, Joseph T: Drumragh Y: 1830 Drumragh Tyrone
Moore, Perry T: Clenabogan Lower Y: 1830 Drumragh Tyrone
that’s all I can speculate for you, unless you are very lucky its going to be a church record or similar or avery helpful person to narrow it further for you. Did his military career merit a pension so is his career recorded somewhere?