No, earned Eden Points must be used by the account that generated them. What you can do, however, is save up enough Eden Points to purchase a physical gift card, and then give that to your girlfriend.
I would like to give them to my girlfriend. We both have an account so I was wondering if I could just send them to her some how.
you could also just send her something if her gift registry's are activated. I've received gifts from my girlfriend AND a stranger sent me something once too! gift registry is quite a way to spread the love!