how can i fix the wire?

I agree with Th.

Be very carefull that you don't invert the polarity. Luckily, the whires inside the cord are colour coded.
I'd use the heat shrink as a finishing touch, and start by using electric tape on the individual whires and put the heat shrink over everything to provide added protection and solidity.

Electro
January 2012

probably.As long as the wires are able to be soldered together and covered with heat shrink

Th
January 2012