There is only one James Sherman in the 1901 census b. ca. 1852
There is no James Sherman in the 1911 census.
The only James Sherman (b. ca. 1847) in 1891 is in St. James Parish, Charlotte Co.
In 1881 there were two James Sherman's; James Sherman b. ca. 1845 in St. James Parish and James W. Sherman b. ca. 1863, in St. David Parish (s/o John and Jersuha.)
In 1871 there were three: James Sherman b. ca. 1849 in Dumfries Parish, York Co., living with John and Rosanna Davis. James M. Sherman b. ca. 1861, in Salisbury Parish, Westmorland Co., NB, s/o David R. and Barbara E. Sherman. James W. Sherman b. ca. 1861, in St. David Parish, s/o John and Jerusha. This is likely the James W. Sherman of St. David Parish who m. 14SEP1885 Sophrona (Sophronia?) Linton. James d. St. David Parish 2JUN1896 age 34 years, 2 months and 5 days.
From this, James Sherman b. ca. 1845-1849 is the same James H. Sherman 1844-1908 and the James in 1901 b. ca. 1852. Also he died between 1901 and 1911, i.e. in 1908 as on his headstone.
A James Sherman b. ca. 1818 d. Fredericton JAN1894. Possibly the James Sherman m. St. Mary's Parish, York Co., NB 25AUG1872 Matilda Bell. In 1881, in St. Mary's Parish, they are James (ca. 1831) and Matilda (ca. 1846) 'Shearman'. I can't find him in 1891. The only James I can find in 1871 in York Co. is the one mentioned above.
While the above is circumstantial it is still heavily weighted to the James in 1901 being the same James buried in the cemetery. I do not see any reasonable alternative. Also, isn't Sarah dead by 1901? So he would be a widower.