Probably not enough wire to solder it back to. you can reopen the JST end and solder it to a wire, but it is a more trouble, and would require some skill with a soldering iron, also you would need more wire than you have to do so comfortably.Strip the end of the black wire and solder it back?
I've just recently learned to solder and it is a lot easier than it appears after you watch a youtube video and practice a little.
There are a ton of tutorials on youtube, here's one I found: