Hoffensberg was educated as a typographer in W. Laub's book printing business in Nykøbing Falster and later worked as an assistant in the Ministry of Defence.

The firm merged with Otto Schwartz' Eftf.s (E. Jespersens) book shop and Em.

Bærentzen & Co.'s lithographic workshop under the name Hoffensberg, Jespersen og Trap in 1874.

The firm was two years later converted into an aktieselskab under the name Det Hoffensbergske Etablissement.

His second wife was Emma Josephine Margrethe Withusen (1835-1926), a daughter of farmer Peter Nielsen Withusen (Berring) of Rygård at Hellerup (c. 1806–47) and Emilie Jacobine Klepser (c. 1811–95).