Change Old Apple Id to @me.com

You cannot transfer purchases. So that is not an option. But you can just get another free email address and change the login address for that old ID and just keep using it.

See -> Change your Apple ID - Apple Support

Just change it to a free Google, or MS, or Yahoo, or whatever free email you want to use.

Oh, and btw, even if you did not change it to an active email address, it would still remain a perfectly functional AppleID. Once created and verified, an AppleID’s use as an AppleID is not dependent on the email remaining an active email. But, if inactive, you won’t get any mails from Apple (e.g. purchase receipts), and if you ever need to recover the account, it may be problematic without a working email address.

If you have changed your ID or password, have you followed the steps in this article?

What to do after you change your Apple ID or password - Apple Support.      

You can try setting up Family Sharing between the IDs if you want to be able to share purchases made with the IDs.

Family Sharing.         

Family Sharing - Set up.       

Yes, I a, sure they cannot transfer purchases. Consumer law and third party licensing does not allow them to do so.

And if your still getting Apple mail at the old email address, then it is still listed as your primary email. Did you follow the instructions in that “change your AppleID” support document exactly? If you did, then that old email should no longer be associated with any AppleID at all.

You need to change the Apple ID email address to a working email address so you can receive emails to the address. See the article Michael posted earlier. In the last sentence of Michael's first post, he explained that you wouldn't receive email if you retained a non functional email address.