How to replace just the iPhone 5S home button cable?

Recently I purchased a home button ribbon cable from iFixit for my iPhone 5S: iPhone 5s Home Button Cable Assembly

However, after removing the home button successfully, I cannot figure out how to release the cable from the original button to allow for the new cable to placed within the original button. I've had little success finding information online and almost everyone uses an already constructed home button assembly in all the repair guides I can seem to find.

Any help you can provide would be greatly appreciated!