This got me curious so I tried doing some searching as well. I am not sure if this has always been the case, but the Salvation Army wear black buttons on their tunics and overcoats, and spell out "Salvation Army" going around the button.
This listing will show a couple of them (hope the link works).
https://www.ebay.com/itm/17476937625...p2047675.l2557
Then I found this listed as a Women's Salvation Army tunic button. But it has only the "S" on it.
http://www.treasurenet.com/forums/wh...nn-button.html
Basically, I seem to have come up with nothing finite. I did look at some 1920's photos on line of SA workers and they all wore the hard rubber black buttons. I also tried the maker and again drew a blank. Lastly, I have enquired through an historical society for Lesher Whitman and maybe they can help.
Sorry I can't be any help, but will follow the thread to see if it gets a finite answer.
Terry