This paper extends the extension theorem for localic real functions of [J. Gutiérrez Garía and T. Kubiak, General insertion and extension theorems for localic real functions, J. Pure Appl. Algebra 215 (2011) 1198-1204] from complemented sublocales to arbitrary sublocales. As an application, the theory of point-free C-, C^∗- and z-embeddings is revisited.