Is it possible to Merge data between an iPhone backup file and an iPhone in use which has never been synced or backed up without losing data or information?
iPhone 6s, iOS 9.1, Mac Mini running El Capitan
No. You can't do that by performing a backup. Depending on the data that you want to transfer, iCloud might work, emailing or using DropBox may be feasible. iOS File Sharing is another way to get files from one device to another by using iTunes.
About File Sharing on iPhone, iPad, and iPod touch - Apple Support
No, the backup completely replaces the contents of the iPhone.
Data on the iPhone can be moved to another location, I.e., Dropbox, before the backup restore.
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How to truly Merge iPhone backup file & not lose data currently on iPhone
