Buy new litter boxes, possibly two. And let Felix have a room for himself. Don't allow Annie to go there. Keep Felix in that room and play with him until he is dead tired. Only then let him out to rediscover your home. Once he attacks Annie, put him in his crate until he calms down (if you don't have a crate use the room.)
When you let him out and he attacks again, put him back in until he's calm. Let Annie have the chance of sniffing him in his crate only if she dares--don't force her to do so. After all, it was her house before his, am I right? I am picturing Annie as a kitten and Felix as a cat because I'm not sure of their age. Annie should feel at home, and Felix should learn to behave. If necessary, spray him with a water bottle whenever he tries to attack her.
When he walks without hurting her, give him treats and use either a clicker or a praise word so he recognizes it just happens when he displays the certain behaviour (walk by the other cat, do nothing, get parent's attention and have a delicious treat) Show him that whenever he attacks, fun stuff stops. The free house space is gone, and treats are taken away. He gets locked up as soon as fighting starts, of course with water and scratching posts and the like, but gets ignored by humans until he's calm.
When he calms down, play with him and use the time to rub a towel (recently rubbed on Annie) all around his body. If possible, also play with him with it. Show him love and attention on a regular basis--he just doesn't get out of the room until he's calm. He should get the idea and behave more after a while. Thank you.