Augusta was born Dec 20, 1873 supposedly in Essen, Nordrhein-Westfalen, Germany. Essen is northeast of Dusseldorf about 50 miles in the west part of West Germany. As you can see from the post from her marriage license, Adolph Klem and Katherine Miller are her parents. According to that 1920 Census, she immigrated in 1886 at age 13 and was naturalized in 1898.
It is unclear whether she came with her parents as I have backtracked the other Klems prior to 1900 of Rochester, NY and find no connections. My hunch is she came to visit and live with distant relatives of the Klem line.
Augusta died on May 21, 1969 and is likely buried in Rochester. Will do more research on that aspect.
Because Augusta immigrated 6 years prior to Ellis Island records, standard shipping/immigration records need to be check to see if further light can be shed on Augusta.
Since she was naturalized in 1898 upon.... likely upon her May 15, 1898 Marriage to Arthur Ed Stallman (middle name often shown by other researchers as "George" since there was an Arthur George Stallman in Rochester. Understand that a G and E in old script look similar so error by other researchers are common.)
For further confirmation, located the Rochester, Monroe County, NY naturalization records. They are likely kept locally because it was not until 1902 until all naturalization papers were forwarded to the Federal Court system. Thus, ask local Monroe County, NY historians for records on naturalizations + or - 1 year from 1898.
The naturalization records often indicate parents and the town of nativity for parents and the child Augusta.
Understand that the Arthur George Stallman, referred to above, is not the same as Arthur George Stallman born 1898 and the son of Arthur E. Stallman.
I presume you know the kids of Arthur & Augusta as:
Arthur George, Leslie Klem, Florence Augusta, and Custer Stallman?