One of Alwin Schroeder’s students at the Leipzig Conservatory was Hugo Schlemueller (1872-1918), the son of a Leipzig music critic. There Schlemueller also worked with Julius Klengel, graduating from the Conservatory in 1891. In the 1890s he played briefly in orchestras in Leipzig and Munich, toured Germany and Russia as a soloist, and taught at the Conservatory in Gotha, where he might have worked alongside cellist Luise Wandersleb-Patzig and may have studied with her. (Or he may have studied with Wandersleb much earlier, before his Liepzig education; a brief 1903 Schlemueller biography that he likely wrote himself makes no mention of Wandersleb-Patzig.) In 1898 he became a disciple of Hugo Becker, and from 1902 he taught alongside Becker at Dr. Hoch's Conservatory in Frankfurt.
It must have been an interesting reunion when his earlier teacher Alwin Schroeder returned to Germany and took over Becker’s Frankfurt cello class in 1907, upon Becker's departure to Berlin. (1907 was the same year that the young Frankfurt-born Paul Hindemith took his first Hoch Conservatory audition.) Schlemueller remained on the Hoch Conservatory faculty until 1917, when he enlisted in the German army. It isn't clear whether his death the next year was due to any injuries he might have sustained in the war.
Schlemueller composed an impressive array of cello pieces, ranging from less-taxing miniatures to virtuoso concertos, and is said have had great success performing his flashier compositions in public. His two-volume Etuden-Schule, a progressively-ordered compilation of 91 etude excerpts by earlier cellists (with generous helpings of Romberg and Kummer), may have helped Schroeder crystalize his own conception for the 170 Foundation Studies for the Violoncello. Schlemueller's later cello works were touted as an "ideal cello school": "With their gradually increasing difficulty and their systematic, technically demanding nature, these works form an ideal cello school for teaching, which gives the teacher a convenient, welcome, and stimulating relief from dry technical studies. Every student plays these melodic, amiable, and humorous pieces with great enthusiasm and pleasure." (From back cover of Schlemueller's Elegie, Op. 18, No. 1)
Today, string music by Hugo Schlemueller is included in teaching curriculums around the world. Designed for younger, developing cellists, his brief character pieces have also been transcribed for viola and doublebass. Some of the original Zimmermann editions of Schlemueller, including the Six Easy Concert Pieces, Op. 12, are distributed by Schott. The Carl Fischer Co. brought out early U. S. editions of his music and still carries a number of his pieces. The recent resurgence of interest in his music has been encouraged by publications such as Volume 1 of Carey Cheney’s Solos for Young Cellists (Alfred Publishing, 2003) and Mary Ann Ramos’s Repertoire Classics for Cello (Carl Fischer, 2014), each containing three Schlemueller pieces. Similiar Schlemueller selections are found at the end of Amy Rosen’s My First Schroeder (Carl Fischer, 2006), a compilation of first-position materials by Alwin Schroeder's older cellist brother, Carl. Schlemueller’s Etuden-Schule is also available in a modern reissue, minus its original narrative explanations.
Especially popular in Europe, Schlemueller’s Perpetuum mobile, Op. 20, No. 6, is one of a set of six Charakterstucke written entirely in the first and fourth positions, without extensions. The solo part can be seen here, but I haven't been able to find the piano score. Sergey Antonov has recorded an arrangement of this piece. The YouTube performances of Perpetuum mobile feature cellists in the under-10 age group. I had trouble picking just one interpretation to share here, so here are links to all of them!
Luisa Wilk and her brother Leo (Germany)
Misha Synchyshyn (Ukraine)
Mari Hakobyan (Armenia)
Kristijonas Grigauskas (Lithuania?)
Since writing this I found some more!
https://youtu.be/81PyAKVBKnU Kaya Ercan (Turkey?)
https://youtu.be/dp9RkSf4gSY Natan Slezak (Poland?)
https://youtu.be/1AD8bBMAq5w Rácz Aladár Zeneiskola (Hungary?)
https://youtu.be/vEeJqANaRWE on doublebass (Hungary?)