Hello CSP
You can certainly help your friend; you do need to contact the DWP first. If you telephone them (I'm sure they'll answer the phone some time!) and explain the circumstances there should be no problem with asking for an extension - usually they will give you two weeks.Follow your telephone request with a letter explaining the circumstances - don't forget to put your friend's name and national insurance number on the letter.
A very delicate question, your friend hasn't been issued with a DS1500 has she? If she has, this is a special circumstance that can speed up any applications, and you will need to make the DWP aware of this. PLEASE be careful if you ask your friend about this. I don't want to upset her, but it is important with regard to her claiming.
Is she undergoing any chemotherapy or radiotherapy,because if she is you need to make the DWP aware of this also.
I am so very sorry your friend is having to go through this. If we can help at all please get back to us. and all good wishes to your friend.