how to free up apple id from a broken iphone for use of imessage

If you don't remember the Apple ID and password, see if you can recover the ID/password. An iCloud e-mail address is an Apple ID. Use every email address you can think of.

Apple ID - How to find your Apple  -  

Apple ID - Find  -     

Other ways to find your Apple ID

You can check to see if you're signed in to the App Store, FaceTime, or Messages on your iPhone, iPad, iPod touch, or Mac, or check to see if you're signed in to iTunes for Windows on a PC. You can also go to iCloud.com or appleid.apple.com and see if your Apple ID prefills on the sign-in screen.   

If you forgot the Apple ID (iCloud) password, enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option if necessary. Link to contact Apple Support at the end of the 2nd article.

Apple ID - Manage

Apple ID – Forgot Password  *      

If you have 2 Factor Authentication enabled, if you can't recover the password using the steps above, you will need to use Account Recovery. The Recovery Process is an automated process and the length of time it takes can vary a lot. Apple ID Support can only answer your questions. They can't intervene in or speed up the process. The article below has some suggestions to shorten the time the process takes.

Apple ID - Recover your Apple ID with two-factor authentication account recovery.