I provide these hard-won birth and death dates in the hope that a persistent Google search will turn them up. (Much of the little that is out there on Gräfe and his trombone concerto appears to be misinformation.)
May 22, 1840-June 22, 1880
Source: Schnebel, Hanns-Helmut. "Auch Militärmusiker litten Hunger: Friedebald Gräfe (1840 bis 1880) und sein 'Konzert für Posaune.'" Bayerische Blasmusik 55, no. 11 (2004): 4-6.
For my translation of this, see Schnebel, Hanns-Helmut. "'Even the military musicians went hungry: Friedebald Gräfe (1840-1880) and his 'Concerto for trombone.'" Trans. Steve Perisho. International Trombone journal 46, no. 3 (July 2018): 32-33.
Cf. Robert Reifsnyder, "The Romantic trombone concerto and its place in the German solo tradition, part II," ITA journal 15, no. 3 (Summer 1987): 35, which states that "Gräfe may have been a violist employed by the Gewandhaus orchestra from 1853 to 1859. If so, etc." (italics mine). By the time the identical claim appears in Noël Lopez, "La épopée du trombone," écoutervoir no. 136 (avril 2003): 20, the subjunctive has disappeared. Yet if Schnebel is right (and his article is based on archival research), the real Friedebald Gräfe would have been about 13 years old in 1853. (One sees also references to 1875-1920. And so forth. Misinformation, apparently, abounds.)