  A group $G$ possesses the Magnus property if for every two elements $u$, $v
\in G$ with the same normal closure, $u$ is conjugate to $v$ or $v^{-1}$. O.
Bogopolski and J. Howie proved independently that the fundamental groups of all
closed orientable surfaces possess the Magnus property. The analogous result
for closed non-orientable surfaces was proved by O. Bogopolski and K. Sviridov
except for one case that was later covered by the author. In this article, we
generalize those results, which can be viewed as Magnus extensions for free
groups, to a Magnus extension for locally indicable groups and consider the
influence of adding a group as a direct factor. For this purpose, we also prove
versions of the Freiheitssatz for locally indicable groups and of a result by
M. Edjvet adding a group as a direct factor.
