Easy Peasy.
Get a couple of crimp on wire connectors and splice in a couple inches of new wire.
I like the wire tap style... they're designed for adding a "Y" connection, but they make a nice positive connection. The butt splice ones are more difficult to get really solid. When you're done, carefully apply some liquid electrical tape to all the connections to keep them dry.
Solderless Wire Quick Splice Connector - 18-22 Gauge - 25 Pack: Amazon.com: Industrial & Scientific