Arthur, I believe, most likely died in Waterborough Parish, Queens County, New Brunswick. At the time, probate courts were on a county by county basis; thus his will would be transcribed into the Queens County Probate Books. The books for 1789-1880 are on microfilm F-1329 at the provincial Archives of New Brunswick in Fredericton. these films are usually on 35 mm film, and can be loaned by interlibrary loan. You may also wish to consult the county Probate Court Files 1788-1841 on microfilm F-10441.
The PANB web site is at:http://archives.gnb.ca/Archives/Default.aspx?culture=en-CA
for contact and other information.