The easiest way to transfer Live Photos is to use AirDrop.
Starting with macOS Sierra 10.12.3, Apple added a new Live Photos Smart Album to Photos. It can be accessed either from the Sidebar (⌘ cmd ⌥ opt s) or in Albums view (⌘ cmd 4).
Once you’re in there, select all the Live Photos you want to transfer, then right-click, Share → AirDrop.
To use AirDrop, you will need one of the following models of Macs:
- MacBook Pro (Late 2008) or later, excluding the MacBook Pro (17-inch, Late 2008)
- MacBook Air (Late 2010) or later
- MacBook (Late 2008) or later, excluding the white MacBook (Late 2008)
- iMac (Early 2009) or later
- Mac Mini (Mid 2010) or later
- Mac Pro (Early 2009 with AirPort Extreme card, or Mid 2010)
Apple has a support article that may help you identify which model Macs you have.
If your Mac doesn’t support AirDrop, but hers does, AND you’ve managed to free up space on your iPhone, she can also AirDrop those photos to your iPhone. You can then import them into your Mac by plugging in to USB.
Barring all of the above, then you can have your girlfriend send you those Live Photos by iMessage, then import them into your Photos Library.
As of macOS Sierra 10.12.4 and iOS 10.3.2, AirDrop and iMessage are the only built-in ways to share Live Photos while preserving their full quality. Using a Shared Photo Album will down-sample your photos to 2048 pixels on the long edge.