Your friend is wise to plan this ahead of time. I would start giving
her (the cat, not the friend!) Rescue Remedy in her water now. It's an
herbal blend that you can find at health food stores and even
Walgreens (near the sleep aids). Also, have her get a Feliway diffuser
to plug in the room she'll be in.

During the move, I would keep her shut in a bathroom in the old
apartment. Like another poster said, put a t-shirt or something you've
worn in with her. Put a big sign on the door that says "cat inside. do
not open" so mover don't let her out accidentally.

Before you move her to the new place, set up a room for her with all
of her favorite things. Because she's a nervous cat, you might need to
keep her confined to this one room for a few days until she's settled
in. Don't rush her. Let her investigate as she feels comfortable. Keep
up the Rescue Remedy and Feliway for several weeks to a few months.
However long it takes her to get comfortable in her new place. Slowly
let her explore the rest of the house as she's ready.

IMO, I would not use valium or any prescription medication on her.