Torque or no torque? Simple charged particle motion observed in different inertial frames

In a given inertial frame, a charged particle initially at rest moves in the central electric field caused by a fixed charge at the origin. The particle has no initial angular momentum and experiences no torque. However, in an inertial frame moving with a nonvanishing velocity with respect to the first, the charged particle’s motion is subject to the Lorentz force with both electric and magnetic fields produced by the “fixed” charge, which is now in uniform motion. The charged particle experiences a torque from the magnetic part of the force; its nonvanishing angular momentum changes in time. This puzzle is analyzed in detail from different reference frames. The chief characteristic of the motion, independent of the choice of the inertial frame, is the constancy in time of the orientation of the relative coordinate r as the particle moves with respect to the fixed (or uniformly moving) charge.