We give a description of the terms in the Ringel-Hall product of preinjective Kronecker modules. We characterize in this way
all the short exact sequences of preinjective modules. As an application we also give an explicit solution to the column completion
challenge for pencils with only minimal indices for columns (corresponding to preinjective modules) and to the row completion
challenge for pencils with only minimal indicies for rows (corresponding to preprojective modules).