Instead of transferring ownership of your Google Apps data, a process which is not provided by Google with a "right-click" simplicity, you can migrate all of your Google Apps Account data to another Google Apps Account.
The result will be equal of what you are trying to do.
This article in Google Apps Administrator Help gives explanation for migrating data between Google Apps account (Contacts, Calendars, Drive files, Sites, Other Google Apps)
Migrate Emails between Google Apps accounts
The data migration service is the recommended way to migrate mail.
It's clientless and cloud-based and easy to set up and monitor. You do
everything in the Google Admin console.
Google Apps Migration for Microsoft® Exchange (GAMME) is a utility
that migrates your mail, including labels and archived mail, to
another account. GAMME can also migrate other data, but requires you
to install the tool first.
You can export Gmail contacts to a CSV file and then use that file to
migrate your contacts.
[..] You can also download all the calendars in your My calendars list or you can choose to share individual calendars
with email addresses in your new account. See Export your
calendar for details.
Migrate Drive Files
[...] you can use the Drive REST API to export and import documents.
You can share individual sites with an email address on your new domain and then transfer the website to Google Apps.
Migrate other Google Apps
There are options for migrating data from other Google Apps products. See Moving product data for details.