It depends on the war type. If it was for a claim only the father but not your heir has, then the war will of course be invalid as the son/heir has no basis for said war.

If on the other hand it’s just a holy war/conquer war/crusade those will keep going through the generations

Are their certain conditions you need to meet in order to win a war you’ve declared? My army was vastly superior to those who I went to war with. I was going through their army like a hot knife through butter, then I died (not in battle) and my son took over. But the war ended, does the war end if I die?

I assumed it would just continue..

Winning a war conditions?