Just a follow up to my most, the problem has been solved! After purchasing "Better FBX importer" on blender market, I wrote the developer and he responded with this
"Though 'Better FBX Add-on' can export Auto-Rig Pro armature, it is not re-targetable, I recommend that you use Auto-Rig Pro to export to FBX file.When using Auto-Rig Pro, after adding the armature, then click 'Match to Rig' enter 'Object' mode, select the character and the armature, bind the character to the armature.
Select the mesh and the armature, then click 'Export FBX...' button, check 'Selection Only' and uncheck 'Bake Actions', then export.
I have tested the workflow, the exported armature and the character is good."
It worked perfectly! Leaving this here for anybody else who runs into this problem.