Connect fingerprint scanner to my computer.

For my project I am using my gt-511c1 fingerprint scanner and use the scanners windows application and store the fingerprints to my computer. I also purchased the recommended jumper cable to connect to the scanner and I also have a rs232 usb ftdi converter.my problem is I wish to use the ftdi convetrer to connect my scanner to my computer using the jumper cable but the connecting cables on the jumper cable seem to look incomaptible(Unconnectable) with the side to be connected on the ftdi conveter.My knowledge in electronics needs a lot of work on and hence I am really unsure of what to do.

1.)Fingerprint scanner:Fingerprint Scanner - TTL (GT-521F32) - SEN-14518 - SparkFun Electronics
2.)Jumper cable:JST SH Jumper 4 Wire Assembly - 8" - PRT-10359 - SparkFun Electronics
3.) MY ftdi usb conveter: http://mcdn01.gittigidiyor.net/15915/tn30/159153159_tn30_0.jpg