Ok, finally, I reached this step so far. From around 5:10, she put the character’s position back and controls to let him jump. The control rigs are all stuck with him properly.
If you are using a custom character with different body proportions and binding pose, after changing the mesh, you need to “refresh” the mesh, compile and save. Here is a video with a custom DAZ character, rigged to UE4 skeleton starting at time 10:00: