Welcome to Android Central! Sorry, I don't quite understand your question. Since this wasn't your phone to begin with, I would strongly suggest resetting the phone. It's not a good idea to continue using your son's Google account on that phone, because you might inadvertently add or delete information from his account, or he might delete some piece of data you wanted to save (but was saved to your son's account, not yours). Do the following:
1. Go to Settings>Accounts-Google, select your son's Google account, and tap Menu>Remove Account.
2. Go to Settings>Backup & Reset, and tap Factory Data Reset.
3. After the reset is finished, proceed with the Setup Wizard, but enter your own Google account information.
Now proceed with installing any apps that you'd like.