Looking for help to confirm OR refute my assumption that Battery A was mustered out July 10, 1865.
Dyer's Compendium of the War of the Rebellion states battery was mustered out July 3, 1865 but I think its based on a misinterpretation of two lines (see below) from the battery's history in the Illinois Adjutant General Report (1861-1865). The battery ARRIVED at Chicago on July 3 not necessarily musteed out that date.

"were ordered home for muster-out, arriving at Chicago July 3, where we received a royal
welcome at the hands of our friends, who gave us a grand banquet in honor of our return."

The Illinois descriptive rolls routinely lists battery members who were serving in 1865 as mustered out on July 10, 1865.