Pickup Question: need some help on a Squier VM Jazz

[Loki182]

I am attempting to replace my squier vm jazz 70's body with the squier fretless vm body. When I was taking the pickups out of the first body, the black wires disconnected from the pickup at the solder joint on both the neck and bridge pickup. When I went to re-solder the wires in there, I noticed the single thread of copper wire that wraps around the pickup was no longer long enough to reach the wire that goes to the control plates. What can I do about this. Can I solder the thick wire directly to the copper wrapping the pickup or do I have to get a thread of copper to come out of the wrap to that "hole" on the plastic portion of the pickup? I can get some photos if necessary.