Q: iTunes not syncing (Authorisation Problem)

Howdy R4PH4HB,

I understand that you're not able to sync your iPhone because of repeated prompts regarding authorization. So far you've done an excellent job of isolating the potential for another Apple ID that may have been used for purchases. I've outlined another process below that may help remediate the situation.

1. Quit iTunes and any other open applications until only Finder is open.
2. From the menu bar at the top of your screen, choose Go > Go to Folder.
3. Type /Users/Shared/SC Info into the window.
4. Click Go.
5. If Finder is not already set to column view, set it by choosing View > as Columns from the menu bar at the top of your screen.
6. Find the SC Info folder. Click and hold on it, and drag it to the trash.
7. Restart your computer.
8. Open iTunes.
9. Authorize your computer. If you have multiple accounts or Apple IDs, authorize your computer for each account.

Windows

1. Quit iTunes.
2. Press the Windows key or Ctrl + Esc.
3. Click the Start search (Windows 7) or magnifying glass icon (Windows 8).
4. In the search bar, type %ProgramData%, then press the Return key.
5. Show hidden files:
   Windows 8: Click View, then click Options. On the View tab, select Show hidden files, folders, and drives.
   Windows 7: Click Organize, then Folder and search options. On the View tab, select Show hidden files, folders, and drives.
6. Navigate to the SC Info folder.
7. Open the Apple Computer folder, then the iTunes folder.
8. Right-click the SC Info folder and choose Delete from the pop-up menu.
9. Restart the computer.
10. Open iTunes.
11. Authorize your computer. If you have multiple accounts, authorize your computer for each account.

 If iTunes repeatedly prompts you to authorize your computer - Apple Support

All my best