From 1949 to 1990 Fuller was a member of the "Society of Old Testament Studies (SOTS)". Among his involvement in major professional projects was the co-founding of the "Catholic Biblical Association of Great Britain" (CBA), of which he then was Hon. Secretary from 1940 to 1965 and chairman from 1968 to 1982. As representative of the CBA he acted in 1963 as Promoter of the English spelling of Biblical names for Catholic use to the Conference of the Bishops of England and Wales (e.g. Noah, Elijah, Joshua, in place of Noe, Elias, Josue as in the Douay-Challoner Bible, based on the Latin text).