A non-Jewish woman converts to Judaism, marries a Jewish man, and has children. She has told her children that she was converted by an Orthodox beit din, to be sure that her children are all recognized as Jewish, even in the state of Israel. The woman has died, and her widower is old and has cognitive problems and can't remember details about the conversion. How can the children find out - where/by whom she was converted - whether her conversion is valid, recognized, and binding - whether the State of Israel will recognize the children as Jewish.
There should be documentation as to which bais din did it and when along with the kesuvah since the rav who married them would have verified the situation. Check the location where the kesuvah is stored.
Also check with the rav (if he is still alive) or whoever now has his records. Many rabbis have sent copies of their records to the Rabbinical Council of America. If the rabbi is no longer available, the records of the wedding would be kept with the synagogue of that rabbi or turned over to his successor.
The kesuvah will ordinarily have been kept by the married couple and may be with the documents such as the wills.
I had encountered a similar situation many years back in Israel and the woman did a gerut (conversion) misafek (from doubt) to make sure everything was valid. While it would be a hassle it enabled her to marry in Israel. The RCA could help with that if no documents were found