I too am researching the Carroll's from Fall RIver, Massachusetts. I have copies of the old Fall RIver City Directories for the Carrolls, Flynns, Hanleys. What intrigued me about your message was that your grandfather moved to Brooklynn, NY. I have some Carrolls that also moved to Brooklyn, NY.
I found a Henry J. Carroll in the 1919 City directory listed as boarding at 115 N. Eighth St. (USA). Looks like he enlisted in the Army in WWI. This is the last year that I have of the directories.
I have a web site http://people.ne.mediaone.net/dflynn51/http://people.ne.mediaone.net/dflynn51/ . It is best viewed with Internet Explorer. I'm having problems designing with NEtscape. On the web site, the section "From Fall River to Roscommon" is the section you want. Under Chapter 1: Ancestors of James H. Flynn, there is a lot of Carroll information. Alsoin Chapter 6, Hanley Carroll Descendants there is a lot of Carroll info from Fall RIver.
Do you have any info on your grandfathers parents , brothers or sisters?