Hi Nathi,
Take a look at Dwayne’s **Edit** comment. This will be the issue.
There is a mirror modifier on the mesh, which is above the armature modifier (as it should be).
But you might remember that the mirror modifier will mirror the .L weights into a .R group ONLY if that vertex group already exists (it will not create it for you).
So just create the group called DEF-Hand.R and the modifier will do the rest.
