Procedures for recording holidays obviously vary from company to company so nobody can really tell you how your company operates apart from people from within.
However, here�s another idea � why not just come clean and tell your new manager you have noticed the mistake.?After all, I�m sure this is what you would do if the mistake was not in your favour. Your new manager should (if he or she is worth their salt) commend you for your honesty and you, in turn, can feel good in yourself.
I suppose I hold some rather old-fashioned values but, when mistakes are made I do not always try to gain ground from somebody else�s error. Just a thought.