Push the tip of the magnet wire a small distance into the molten solder and hold it there for a few moments. The solder will bubble away the enamel and tin the copper underneath in the process.

tinned copper, PVC insulated, ring band stripe color coded, aluminum-polyester wrapped shield around 4 conductors with stranded drain wire, polyester tape over this shielded group, 21-22 AWG (7x30) ...