Legal Question in Real Estate Law in California

No. Your father's estate must be probated. The property will then go to your mother and the quitclaim will then be retroactively validated to make you the owner. However this is going to have some pretty bad tax consequences for you in the long run, and will trigger a default on the loan. So if you have not already recorded the quitclaim you REALLY should not, and you should get some good tax and probate advice before you make a real mess of things.

I agree. A letter from your mother has little significance. The issue is what the actual chain of title reflects. This may require dirffering steps, depending on the precise form of title. As noted, a probate may be necessary. It is possible your parents held title in joint tenancy, and if so a simpler process may be available, but this has tax implications . Seek good estates counsel.