How do I import an other family members photos to my iCloud account?
There is no direct way to do what you want.

You don't state if you use iCloud Photo Library. If you don't, you can enable that and select the Optimize Device Storage option as @JaimeSantaCruz suggested. That will reduce the amount of space required on the device but will not eliminate it entirely.

There are a couple of workarounds but neither are ideal.

You could create a shared album, have her share everything she has on her device, then remove her from the shared album (and she can delete all the photos on her phone). The problem is that shared albums reduce the size of the pictures, so you won't be getting the originals.

If you have a Mac, the Photos app could be utilized, but it depends on your current set up. If she uses iCloud Photo Library already and the Mac is set to use the same iCloud account, everything should be in Photos already. If not, you'll need to hook up her iPhone to the Mac, and import everything. In either case, once everything is in Photos, you could copy all of the items into a new, non-iCL library (or an iCL library in a different user account that's hooked up to your Apple ID).