144 hour transit visa. My friend is coming to visit me from England

That depends on whether you yourself have registered at the local police station. If you have registered then all they need to see is your friends passport, arrival card, your passport as well as your residence permit. If you haven't then it's probably a good idea to register yourself first.

Thank you for your help. Yes I am registered I have a work permit and residency.

Does she just need to send her a photocopy of my residency and passport?

Do I have to give her a letter or anything?

Unfortunately registration is only done in person and you and her will have to visit the police station together after her arrival with the original documents. (AFAIK they don't accept photocopies and will scan or photocopy the documents on the spot instead.)