Does a magnetosphere mean an active core?

A Magnetosphere is a planet or solar body's internal magnetic field, solar wind plasma, and interplanetary magnetic field (IMF).

The Galilean moons would've been a possible destination for man, the only problem is the intense radiation and tidal forces from Jupiter. Callisto and Ganymede are likely destinations that can harbour life

And I think I'll do a post on the habitability of Moons