Hi, I'd like to help you with your question.
I am so sorry to hear about your sister's husband. My condolences to her and to you.
You can help her in many ways. If there are still things she needs to complete regarding her husband's arrangements or any other tasks related to his death, help her by either doing them for her if she desires, or helping assist her to complete them. This will take a big burden off her.
Just be there. This is the most important thing you can do for her. Let her talk and support what she says with affirming comments such as "I understand". People grieve in many different ways. Some become angry, some depressed, others withdrawal. There is no way to say how she will handle her grief. Accepting what she feels will go a long way to helping her recover.
If she is up for it, take her out somewhere. Make is a place she feels comfortable and just share a coffee or lunch. Maybe even a drive around the town. Anything to help her get away for a bit and get her mind off everyday things.
If there is anyone she needs to notify, help her complete that task. It is difficult for a grieving person to have to repeat the news of a loved ones death over and over.
Her grief may take a while to heal. Some people seem better afterwords only to become distraught again later, after all the activity related to the death has stopped. It is in that time that people often need the most support. If you cannot be there in person, send her cards, books or little gifts and let her know you are thinking of her and have not forgotten her grief.
Finally, bring up the deceased and talk about him in the future. It lets her acknowledge that he was a big part of her life and if she still needs to talk, she will feel you are there for her.
If she continues to grieve after a long period of time and her grief is becoming a depression, see if she is willing to talk with a therapist. There are also groups that help with grief. She may just need a little extra help to feel better.
I hope this has helped,Kate