  We consider static, spherically symmetric, electrically or/and magnetically
charged configurations of a minimally coupled scalar field with an arbitrary
potential $V(\phi)$ in general relativity. Using the inverse problem method, we
obtain a four-parameter family of asymptotically dS, flat and AdS solutions,
including those with naked singularities and both extreme and non-extreme
black-hole (BH) solutions. The parameters are identified as the asymptotic
cosmological constant, an arbitrary length scale, mass and charge. In all
asymptotically flat BH solutions, the potential $V(\phi)$ is partly negative,
in accord with Bekenstein and Mayo's no-hair theorem. The well-known conformal
mapping extends the BH solutions to Jordan's pictures of a general class of
scalar-tensor theories (STT) of gravity under the condition that the nonminimal
coupling function $f(\phi)$ is everywhere positive. Relaxing the latter
condition and assuming $f=0$ at some value of $\phi$, we obtain wormhole
solutions in a particular subclass of STT. In such solutions, the double
horizon of an extreme BH in Einstein's picture maps into the second spatial
infinity in Jordan's. However, at this second infinity, the effective
gravitational coupling infinitely grows.
