Solder the new speaker wires in the same position as the old one.

It is advisable to use a lead free solder

Use a small amount of solder to not mix up the connections and prevent short circuiting.

In case you use a large amount of solder, use a solder wick to absorb the excess solder.

You can find more information on "How To Solder" here:How To Solder and Desolder Connections