Problem: Emma's mother had died long ago, and *her* place had been taken by an excellent woman as governess.

Do "her" and "Emma's mother" mean the same thing?

Answer: yes

Problem: Tom said "Check" to Ralph as he moved *his* bishop.

Do "his" and "Ralph" mean the same thing?

Answer: no

Problem: The father carried the sleeping boy in *his* arms

Do "his" and "The father" mean the same thing?

Answer:
yes