It's a difficult one, the 'IA' mark is indeed a good match, as moonshine has noted, for the one on the Incorporation website, however, the 'ABD' is also a good match for the punch used by John Allen, as shown in Richard Turner's 'Illustrated Directory of Scottish Provincial Silversmiths & Their Marks'.
I suppose there may be several scenarios here. As that particular 'IA' mark attributed to Argo is found, to my knowledge, as a single struck mark on items and the 'IA' punch used in conjunction with the 'BA' appears to be a different one, could the attribution be incorrect? Or as Argo is thought to have spent time in Aberdeen, could the 'ABD' punch be a shared one?
Hopefully another member may add their thoughts.