Magnetic sounding is a powerful tool to explore the interior of planetary bodies through the electrical conductivity structure. The electrical conductivity structure of the lunar mantle has previously been derived from surface magnetic field measurements as part of the Apollo 12 mission and concurrent magnetometer data acquired from orbit through the Explorer 35 satellite. Here, we derive the first global conductivity structure using only satellite magnetometer data collected by the recent Lunar Prospector and Kaguya Selene satellite missions. We show that the field in the geomagnetic tail exhibits a simple geometrical structure and can be well described by a single spherical harmonic of degree and order one. Employing this information about the inducing field geometry and assuming a potential representation of the field in the geomagnetic tail, we derive a frequency-dependent transfer function and invert it for a global one-dimensional (1-D) electrical conductivity profile. Our global transfer function shows striking similarity with the local one obtained from joint analysis of Apollo 12 and Explorer 35 magnetometer data. This indicates the lack of local variations at the Apollo 12 landing site compared to the globally-averaged upper to mid-mantle electrical conductivity structure.