Should we tell her or not?

My husbands biological father passed away Tuesday evening. They had no communication before and his bio father has always been determined to keep it a secret from his life partner. He never wanted her to know or anyone for that matter. But now he has passed away an it was due to Health issues. So for the sake of my husbands health and our childrens health we want to know his bio father’s health history. An if my husband maybe entitled to anything since his passing. In order to do this that means telling his long time girlfriend of 40+ years that not only does he have a son but that he also cheated on her with said sons mother. When should we speak up and how should we go about it bc I feel the sooner the better but my husbands aunt says that not for awhile let her mourn. My thing is I fear if we wait too long after his passing that we won’t have the opportunity to get in contact with her again. Plus it’s be over 40 years since it happened so us speaking up now shouldn’t be as bad as the loss of him.
I don’t mean to sound callus about it but this man knew about my husband and acted like he didn’t exist and he knew of our children as well and still said nothing. My husband is 41 and I feel like something should be said sooner than later. So should we speak up or wait?