Question : DNS Not Updating

We are having an issue when we move a computer from one location to a different building.  The IP address updates on the client to the new address but the DNS records still points to the old address.

How do we get computers that are moved to update their IP address in DNS automatically?

Answer : DNS Not Updating

are we talking about the A records or the PTR records....or both?  Is this new building served by the same dhcp server?