Hello, I'd like to help you with your question.
I am so sorry for your loss.
It sounds like your friend is either fearful of being alone or he is trying to avoid going through the mourning process. People who find a new relationship after the death of a loved one usually are trying to cope. And it sounds like that might be the case for your friend.
This woman could be taking advantage of the situation or her motives could be genuine. It is hard to say. But either way, it is a good idea for your friend's children to talk with their attorney to ask about options to protect your friend's estate and him from being taken advantage of.
You can also talk with your friend and express your concern. Try approaching him by showing that you are concerned for his well being and that you want to be there for him. By supporting him, you open the discussion up for him to talk about anything he needs to. Also, encourage him to hold off on any big decisions and to take the time to grieve over his loss. It can be a difficult balance to know how to be supportive and how to address his new relationship. Keep in mind that just by being there, you are making a difference to him and his family. Stay in his life as much as you can so even if he does choose to continue this relationship and it turns out badly, you will be there to help.
You can also recommend some resources to help him cope. Here are a few to get you started:http://www.helpguide.org/mental/grief_loss.htm http://www.griefshare.org/
Healing After Loss:: Daily Meditations
For Working Through Grief by Martha Whitmore Hickman
Life after Loss: A Practical Guide to Renewing Your Life after Experiencing Major Loss by Bob Deits
I hope this has helped you,