Can I transfer content between devices authorized to different Apple IDs?
Purchases are linked to the Apple ID.

Your devices may only sync content that they are authorized for. They can be synced with any device (up to 10) that is authorized to the ID.

This is an extract from the apple support website:


  If you want to transfer iTunes Store purchases from an iOS device or
  iPod to a computer, be sure to authorize the computer before
  connecting the device.
  
  ...
  
  Important: Clicking Erase and Sync will delete any existing content
  currently on your device. The content will be replaced with whatever
  existing content is in the current iTunes library your device is
  connected to. If there is no content in the iTunes library, nothing
  will be synced to your device, and your device will be empty.
  
  iTunes
  will begin copying any purchases made with any account for which the
  computer is authorized.


Jailbreaking might offer possibilities to bypass the restrictions, but it'll be against apple's licensing terms (copying the content to unauthorized devices that is).

I believe this would require to jailbreak iTunes on your Mac aswell for syncing to work - and I do not know if there are solutions to this.