How to backup Fedora 22 that is encrypted?

edit

You can always backup all files once you login to Fedora and have introduce proper password for the encrypted partition with a regular backup.

If you want to backup the entire partition you can use dd but you a disk of same sice or more to create the backup

dd if=/dev/sdX of=/dev/sdY bs=512 conv=noerror,sync

You can change bs=4096 instead of 512 if you use a bigger block size

You can also set of as file of=/path/to/mbr_file.img instead of disk

Hope this give you an idea or introduce enough curisite for you to investigate more.