I am sharing down below the step by step of the Control Rig I created for my character: the Seagull.
This character already had a Maya Rig, so I wanted to try to replicate the deformations that already existed before, in Unreal. Especially the neck squash and stretching.
This is a post for my future self. When I forget all of this logic behind the matrices, and need to learn it again. Also added a code that does all the job for me, so I don't really need to remember any of this.