How to exact copy paint weights from one object to another 2 object occupying the same space with the exact same geometry.
They both need to be influence by one bone identically. I edited one's paint weight so I want to have the same changes applied to the other.

I was suggested to:
Select the object with the correct weight(source)
Shift select the object that you want to copy weights.
In weight paint hit [ Transfer Weights ] 
Opens the Transfer Mesh Data tab.
hit [ Transfer Weights ] again.

I tested it in pose mode but it didn't work they are still different.


(UPDATE)
Upon additional information 
Hit [ Transfer Weights]
For Source Layer destination select: By Name
For Destination Layers Matching select: All layers
For Mix Mode select: Replace
I know this is 4 years old post but I've found a simpler solution with blender 2.82. So what I do is I copy the mesh that has three original vertex groups and arrange in the space where the 2nd mesh is meant to be at. Then rename the 2nd mesh's all vertex groups to different so it can retain its weight paint from original mesh. I used armature human rig default.