What do you think about me telling my sister to get over her dead friend
That's pretty cold. People mourn differently.
It's been a reasonable amount of time to get over it. I'm pretty sure she's doing it to annoy me.
You should support your sister however long it will take her to stop grieving. Each person is different when dealing with pain.
I think she's going through a mental issue and I'm going to make it my mission to get her to move on with her life.
Do you really think she's faking her pain about her deceased friend to get at you? That sounds a little narcissistic. Not everyone deals with death the same way; you need to support her, not berate her.