Is it permissible to offer condolences to my brother's wife for my brother's (passing)?

It is permissible for a man to offer condolences to his deceased brother's wife. It is also permissible to speak with a non-mahram woman (ajnabiyyah) out of necessity and to the extent of that necessity, provided that there is no fear of temptation (fitnah) and that Sharia-compliant guidelines are observed, especially if she is not young. There is a difference of opinion regarding offering condolences to a young non-mahram woman due to the risk of temptation.