  Using a representation theoretical approach we give an explicit numerical
characterization in terms of Kronecker invariants of the subfactor relation
between two preinjective (and dually preprojective) Kronecker modules,
describing explicitly a so called linking module as well. Preinjective
(preprojective) Kronecker modules correspond to matrix pencils having only
minimal indices for columns (respectively for rows). Thus our result gives a
solution to the subpencil problem in these cases (including the completion),
moreover the required computations are straightforward and can be carried out
easily (both for checking the subpencil relation and constructing the
completion pencils based on the linking module). We showcase our method by
carrying out the computations on an explicit example.
