Training the cat to poop outside

Hi again

Problem two.
My cat was taken from it mother at six & half weeks old. (too young I know) When going to the litter box she won't cover her poop (leaves the covering for the other cat to do) and my girlfriend has decided the cats have to be toilet trained to go outside from now on. The cat hates outside and will do her business on the floor inside (not the carpet yet).

I've got the litter box outside and we are always putting her in there but jumps out like a rocket and wants nothing to do with her litterbox even tho its the same one that was inside (she does'nt seem to think so).

Is there someway I can train the cat to go outside?

Please help