Ensuring Husband Gets My Inheritance If I Die Suddenly

EDIT UPDATE: Someone PM'd me with a satisfactory legal answer involving updating my estate plan. Thank you!

A good news inheritance question, for a change. I am a happily married woman in California. My husband is retired (he's 70) and I work (I'm 57). He gets SSI.

My mother died in December and I am going to inherit one-half of the family trust. My sister gets the other half. This money will ensure a good retirement for both us and my husband's wonderful brother (who has little money due to years of selfless care of a cancer-ridden wife).

The estate is going through the usual paperwork, but the executor, with whom I am in close contact, is ethical and reliable.

Query: if I die before the estate finishes processing, will my husband get my share? I'm trying to figure out how paranoid I should be about my sudden death, and what steps I should take to protect my husband and family. I'm not planning on free solo rock climbing or bungee jumping any time soon, but I can't account for weird drivers.

My husband is named as my inheritor in my estate plan. Thank you for any insight here.