As for this situation, I think you'd better try the 3rd-party program rather than iTunes. Just follow below steps to reach this goal. Download Leawo iTransfer
' Leawo iTransfer for Mac
and install it.
Step 1. Run Leawo iTransfer for Mac and Connect iPhone
Launch Leawo iTransfer for Mac after installing it on your new Mac computer. When the software indicates that you can connect your iOS device, plug your iPhone to Mac via the USB cable. The software will automatically detect your iPhone and show the Libraries on the left sidebar. The files will show on the right part of the window after you choose a library.
Step 2. Select Files to Sync
Choose a Library and then all the files in the library will show on the right part of the software (Set the Music Library as an example). Click the transfer button (the right arrow in a dark-blue rectangle) at the right bottom to transfer all the files to computer. Or you can hold Ctrl key and click to choose certain files, and then right click the chosen files and choose "Transfer to > My Computer".
Step 3. Transfer Settings
After choosing files, a dialog of transfer settings comes out. In this dialog, you are able to check "Transfer to List" and "Save to Folder". Checking "Transfer to List" can make sure your files be transferred to iTunes; Check "Save to Folder" and click "Change" to choose a target folder to save the transferred files. If you are using a new computer and the iTunes is newly installed, I suggest you check both options. After choosing target folder, click "Transfer Now" to start to sync iPhone to new computer.
Step 4. Syncing iPhone to New Mac
When the transfer begins, you will see a dialog of transfer process. A progress bar in the dialog will show you the percentage of the syncing process. When the syncing process is finished, you will find all the files in your target folder and iTunes.
For more detail, check: How to Sync iPhone to New Mac without Losing Data