Good day to you.
Is your problem just in connection?
Such things are often connected with a help of 2.1mm male-female DC power connector pair. How ever, if you want to use connection pair you've got, you have have to supply your freelancers with it mark or more detailed photo. At your second photo a red wire is used for ground wire and black for signal one (usually in opposite way). I can’t say anything about connector pair until I’ve got another photos.
If you hire me, think $20 will be enough for this job.