The goal is to get the rotational difference of the bones between Armature 1 and Armature 2 in its T-pose(not exactly), then apply the difference to a pose of Armature 2.

The purpose is so the model of Armature 1 follows Armature 2.

Testing for just the Right Upper Arm

Lets say I have two Armatures in normal poses. I want Armature 1 to follow Armature 2. The Armature 1 on the Left is the Source and Armature 2 on the Right is the Target:

But the Bones are not Aligned so the rotation is values are different:

First, Save the rotation variable of Armature 2 Right Arm, then set the Right Arm bone vector of Armature 2 to vector of Armature 1

Code:

import bpy
from mathutils import Matrix
from mathutils import Quaternion

context = bpy.context
scene = context.scene
RobloxRig = bpy.context.scene.objects['__Rig'] 
UpperRightArm = RobloxRig.pose.bones["RightUpperArm"]


CloudRig = bpy.context.scene.objects['CloudRig'] 
CloudRig_UpperRightArm = CloudRig.pose.bones["r_uparm"]

def snap_rotation(source, target):

    Ms = source.id_data.convert_space(
       pose_bone=source,
       matrix=source.matrix,
       from_space='POSE',
    )

    Mt = target.id_data.convert_space(
       pose_bone=target,
       matrix=target.matrix,
       from_space='POSE',
    ) 
     
    _, q, _ = Ms.decompose()
    t, _, s = Mt.decompose()

    M = (
       Matrix.Translation(t) @
       q.to_matrix().to_4x4() @ 
       Matrix.Diagonal(s.to_4d())
    )

    target.matrix = target.id_data.convert_space(
       pose_bone=target,
       matrix=M,
       to_space='POSE',
    )    

if __name__ == "__main__":
   context = bpy.context
   scene = context.scene

   scene.frame_set(720) #Frame of Normal pose
   bpy.context.view_layer.update()

   Mt = UpperRightArm.matrix
     
   loc1, rot1, scale1 = Mt.decompose()

   NormalRot = Quaternion(rot1)


   snap_rotation(
       CloudRig_UpperRightArm,
       UpperRightArm 
   )

Output:

Now that Bone Vector of Armature 2 is aligned with Armature 1, Save the new rotation, Set it back to normal and get the rotational difference.

bpy.context.view_layer.update()

Mt = UpperRightArm.matrix
     
loc2, rot2, scale2 = Mt.decompose()

#New Rotation
NextRot = Quaternion(rot2)

#Setting back to normal using from code above values
M = (
    Matrix.Translation(loc1) @
    rot1.to_matrix().to_4x4() @ 
    Matrix.Diagonal(scale1.to_4d())
    )
    
UpperRightArm.matrix = M

#Getting Difference
RotationalDifference =  NormalRot - NextRot

Output, Just back to normal after taking the value:

Now I Change the Frame which moves Armature 1:

scene.frame_set(730)
bpy.context.view_layer.update()

This Final part which Doesn't work I set the vector of the Armature 1 to Armature 2 like before then added the difference.

snap_rotation(
    CloudRig_UpperRightArm,
    UpperRightArm 
)

bpy.context.view_layer.update()

Mt2 = UpperRightArm.matrix
     
loc3, rot3, scale3 = Mt2.decompose()

FinalRot =  RotationalDifference + Quaternion(rot3) 

M2 = (
    Matrix.Translation(loc3) @
    FinalRot.to_matrix().to_4x4() @ 
    Matrix.Diagonal(scale3.to_4d())
    )

UpperRightArm.matrix = M2

Wrong Output:

Here is what's expected:

A small difference is that it applies to all bones. If I get one bone it would be easy to get the rest.

Please help, Thank you.