ANSWER - It depends on your motive for asking him. If you are friends and you are looking to strengthen your friendship in order to support one another through your grief then I see no problem at all in asking him. Equally if you are looking to maintain a friendship with your deceased fiance's family either through respect for him or through your own liking for the family you have grown to know then again that sounds fine to me.
I'd suggest you make it very clear that you are inviting him as a friend and that you are not looking for another relationship at this stage. To be honest even if you do have romantic feelings for this man it would be prudent not to act on them while you are both so recently bereaved. If you do find yourself attracted to him it could be the fact that he reminds you of his brother which is no basis for any kind of relationship. If over time you grow to know him as an individual in his own right and a love does grow then that is different but at the moment you are too emotionally vulnerable to be looking to rush into anything.
My advice would be to be totally upfront, explain you are asking him as a friend and that you are only looking for his friendship. If you don't feel able to do that or you feel that saying that to him might not be telling the whole truth then it might be better to find somebody else to go with.