  We reexamine the dual Abrikosov vortex under the requirement that the lattice
averages of the fields satisfy exact Maxwell equations [ME]. The electric ME
accounts for the total flux and the magnetic ME determines the shape of the
confining string. This leads to unique and consistent definitions of flux and
electric and magnetic currents at finite lattice spacing. The resulting
modification of the standard DeGrand-Toussaint construction gives a magnetic
current comprised of smeared monopoles.
