Junius Booth's child William

[Steve]

From the description of the poster, it sounds more like a Grand Army of the Republic (GAR) recruitment poster, not anything printed during the Civil War itself. The GAR was a fraternal group of Union veterans of the war, like the present-day VFW. GAR officers were elected and their ranks don't have any correspondence to members military ranks during the war.

But I haven't seen the poster, so I can only guess by the description. But the poster said that Booth was living in Mass., but he was living in and enlisted in the Army in Rhode Island.