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In my continuing quest to find improved images of players from the 1888 Western Association, I have turned to the 1887 Minnesota Team photo, shown on Threads of Our Game. Some of the players are identified in the caption.
Back row: Unidentified, George Winkelman, Unidentified, Robert Foster (manager), Owen Patton, John Shaw, Charles Willis
Front row: Miah Murray, George Ganzel, Elias Peak, Elmer Foster, Bill Hawes, William Tuckerman, Unidentified

Possibilities for the unidentified players are John Moriarty, Jim McKeever, and George Meister. It is thought the photo was taken in April, right around the time the season started, as Ganzel was released on April 28.

It happens that the Minneapolis Star Tribune published a preview of the club on February 7, 1887 (pg 3). The players profiled, with sketches, included all of the players named above except Winkelman. On February 28, the club signed pitcher James Allen, and on April 1 the St. Paul Globe noted that Frank Visner was also on the club. This gives a pool of 15 players plus manager Foster who could have been in the photo.

Frank Visner was the brother of "the noted batter and catcher of the same name in the Rochester team" (Star Tribune March 7, 1887), which would be Joe Visner. Joe Visner joined Minnesota late in the season (according to the St. Paul Globe, September 24, 1887). Baseball-Reference lists an O.S. Visner for the club, and it is not clear (to me at least) if this reflects Joe or Frank or some combination of the two. Most likely, it is all Joe, as Frank was reported released on May 5, along with James Allen.

Robert Foster was the brother of Elmer Foster. The resemblance can be seen comparing Elmer to his brother.

Updated proposals 9/26/2021:
Back row: Jim McKeever, George Winkelman, John Moriarty, Robert Foster, Owen Patton, John Shaw, Charles Willis
Front row: Miah Murray, George Ganzel, Elias Peak, Elmer Foster, Bill Hawes, William Tuckerman, George Meister