How do I let other users on my MacBook Pro update apps that I've downloaded?

I recently left a position as an IT at a school district where I was put in charge of all Mac products district wide. Most of the important apps, such as Apple Configurator or Remote Desktop, were downloaded using a district Apple ID, but many of the apps downloaded (regrettably) were through my own personal Apple ID. Is there a way to allow other accounts on the computer to update these apps without my Apple ID and password? If not, is there a way we can at least re-download those apps via the district Apple ID and transfer the data to that one? Running Mac OS 10.8.5 on a mid 2011 MacBook Pro. Thanks in advance for any help. 🙂