SO this is what I have found:
1. Open iTunes - (I'm not sure for what, but this is what they said on Apple page)
2. Plug in your iPhone
3. Open Photos App - (the one with a colorful flower as an icon)
4. Make sure you have a full screen, if not then in the middle of the screen on the top you should see Albums / Import / Photos / Projects etc.
5. Choose Import
6. Wait until all photos from your iPhone will load into this app. It might take a while.
7. Choose which photos do you want to transfer and click Import Selected at the top of the screen - if you don't have much space on your Mac - like me - you will have to keep selecting bunch of photos and transfer them, then delete them when they are safe on your external hard drive and keep on doing that until you have all that you need. You can click on delete photos - so when they will import, it will automatically be deleted from your iPhone and Photo App.
8. Change on the top of the screen from Import to Album - there are your imported photos. Select them all.
9. Go to the very top of the screen (black menu) - choose FILE - Export - Export unmodified originals - click to tag Export IPTC as XMP - File name: use file name - subcathalog : Moments / Memory name. Click Export.
10. Choose your externadl harddrive - and file where you want to save it. Click on Export oryginals.
11. Go back to Photo App. Select all photos that you have just exported to your External hard drive. Select them and delete them.
12. Choose Delete at the top menu instead of Album and Import - and also delete them from there or empty your trash bin in Photo App (not on your Mac).