Connecting female thread to female threaded faucet
If we can believe what you wrote in your question rather than what you show in your pictures then what you are really looking for is a M to M adapter. Not the F to M adapter that you linked. Here is an example of an M to M adapter.



(Picture Source: https://www.amazon.com/Danco-10524-Chrome-Aerator-Adapter/dp/B00FI6U81C/ref=sr_1_6?keywords=male+to+male+faucet+adapter&amp;qid=1552209508&amp;s=gateway&amp;sr=8-6)

There are multiple sizes used for aerator attachments. Some of the most common include in metric sizes M22x1, M24x1 and M28x1. In USA sizes you will find 3/4"-27, 15/16"-27 and 55/64"-27. The first number being the diameter and the second the thread pitch designation. So take this into account when you select the proper adapter. Some adapters are actually designed to convert between these sizes including the one that you linked in your question.