When my child was little, she wanted to know whether my parents, who are not Jewish, would go to Heaven. I explained to her that the righteous of all nations have a place in the world to come. But Rabbi Kalman Winter, zt'l, told my wife she could reassure our then young daughter that because I had converted, my parents would have a special place in the world to come. What sources support the proposition that parents of a convert benefit from his or her's acceptance of Torah and mitzvos?
InParshas Lech Lecha - Braishis 15:15 it says that when Avraham will pass away ואתה תבוא אל אבותיך בשלום. Rashi explains that even though Terach was an idol worshipper it says come to your parent, since Terach repented prior to his death.
The Marhasha was asked the following question when he was a child. How does Rashi know that Terach repented. Perhaps he remained a sinner however he received Gan Eden like it says in Sanhedrin 104a ברא מזכי אבא
The Marhasha answered that it says Avosecha אבותיך - Lashon Rabim - plural. That indicates that not only Terach was rewarded with Gan Eden also Terach's father, Nachor received Gan Eden. So you may say that Avraham was able to help Terach get into Gan Eden, however how was Nachor able to get in there? Therefore Rashi says that Terach repented and since a child helps a parent therefore Nachor also received Gan Eden. That is why it says Avosecha אבותיך - Lashon Rabim - plural.
a person is judged primarily for his own choices in life. this can be seen for example by rivka's father or rachel's father who were considered wicked people despite that their daughters were righteous. likewise, Chizkiyahu was considered a tzadik despite that his son Menashe was wicked.
It helps to have righteous descendants, but this is not the primary factor by which a person is judged.