Step 1: Quick Work - Disassembly of Magsafe Connection
The MagSafe connector was already frayed free of the wire on my charger. But I did not have near enough wire to solder back onto. The aesthetically pleasing body of the connector needs to come off.
Out come the pliers (Slide lock in my case) to crush it off. Be careful not to damage the magnetic metal contact up front. We will still need to dig into this further to expose enough wire to solder to.