  We construct new solutions of the Faddeev-Skyrme-Maxwell model, which
represent Hopf solitons coupled to magnetic fluxes. It turns out that coupling
to the magnetic field allows for transmutations of the solitons, however, the
results depend both on the type of the vacuum boundary condition and on the
strength of the gauge coupling. It is shown that the structure of the magnetic
fluxes of a gauged Hopfion is governed by the preimages of the points
$\phi_3=\pm 1$.
