There is more that you can (and possibly should) say.
You could try researching grief support or grief therapy groups available in your area. I think many bereaved people will find these valuable. And I think there is empirical evidence of this. There were a number of studies of the families of the people who died in the infamous Cocoanut Grove fire, "the scene of the deadliest nightclub fire in history. " These families were divided into two groups: the first group were left to fend for themselves, the second group were provided with brief psychotherapy. Then the two groups were studied over a period of up to ten years. The result was that the second group did remarkably better in adjusting to their loss than the first group.
See:
Cocoanut Grove fire - Wikipedia, the free encyclopedia
If you can tell this woman about such support groups in your area, you would be doing her a kindness.
I disagree that suicides are just like any other deaths. There is a thing called the NASH scale, which is short for Natural, Accidental, Suicide, Homicide, which lists the kind of deaths in order of the difficulty of bereavement, from least difficult to most difficult. Suicides are the second most difficult deaths to cope with, exceeded only by homicides.