  We revisit the calculation of the fermion self-energy in QED in the presence
of a magnetic field. We show that, after carrying out the renormalization
procedure and identifying the most general perturbative tensor structure for
the modified fermion {mass operator} in the large field limit, the mass
develops an imaginary part. This happens when account is made of the
sub-leading contributions associated to Landau levels other than the lowest
one. The imaginary part is associated to a spectral density describing the
spread of the mass function in momentum. The center of the distribution
corresponds to the magnetic-field modified mass. The width becomes small as the
field intensity increases in such a way that for asymptotically large values of
the field, when the separation between Landau levels becomes also large, the
mass function describes a stable particle occupying only the lowest Landau
level. For large but finite values of the magnetic field, the spectral density
represents a finite probability for the fermion to occupy Landau levels other
than the LLL.
